{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "e7046532-cdfc-45c6-acc8-1a60747db398",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from shapely.geometry import Point, LineString, Polygon  #original late Jan'22\n",
    "import shapely\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "from scipy.optimize import minimize\n",
    "def tan(x):\n",
    "    return math.tan(x)\n",
    "def cos(x):\n",
    "    return math.cos(x)\n",
    "def sin(x):\n",
    "    return math.sin(x)\n",
    "def r3(x):\n",
    "    return round(x,3)\n",
    "def r5(x):\n",
    "    return round(x,5)\n",
    "def plotPoly(inputPoly):\n",
    "    dummyPoly = Polygon([(0,0),(0,1),(1,1)])\n",
    "    if inputPoly.geom_type == dummyPoly.geom_type:\n",
    "        x,y = inputPoly.exterior.xy\n",
    "        plt.plot(x,y)\n",
    "    else:\n",
    "        for geom in inputPoly.geoms:\n",
    "            if geom.area > 0:  #to avoid error with LineString geom parts\n",
    "                x,y = geom.exterior.xy\n",
    "                plt.plot(x,y)     \n",
    "def plotCenter(t,geom):\n",
    "    plt.text(geom.centroid.x,geom.centroid.y,t,ha='center') \n",
    "\n",
    "pi = 3.1415926535\n",
    "\n",
    "# This code computes the tract usage vs. distance from a boundary vs. two weighting functions that represent ...\n",
    "#  ...how the included angle of the shorted wedge (and its opposite) depend on the degree of shortness\n",
    "# For simplicity, the total district pop is 4, such that a shorted wedge's center will be <1 unit from boundary\n",
    "# The angles always face exactly north,east,south, and west (as they do in HD code after re-orientation)\n",
    "# due to the symmetry about y-axis, we only analyze x>0 areas\n",
    "\n",
    "# July 2023 - NEW -- also explore the idea of sampling more near boundary than center, instead of changing angles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "c4cd60ed-b9fe-40b9-81b0-d1b47b017ae7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.07873 for maxAngle, coeff1, 2 = 144.0 0 0.5\n",
      "RMS error is 0.072479 for maxAngle, coeff1, 2 = 144.0 0 0.55\n",
      "RMS error is 0.067643 for maxAngle, coeff1, 2 = 144.0 0 0.6\n",
      "RMS error is 0.070005 for maxAngle, coeff1, 2 = 144.0 0 0.65\n",
      "RMS error is 0.074419 for maxAngle, coeff1, 2 = 144.0 0 0.7\n",
      "RMS error is 0.078862 for maxAngle, coeff1, 2 = 144.0 0.05 0.45\n",
      "RMS error is 0.07288 for maxAngle, coeff1, 2 = 144.0 0.05 0.5\n",
      "RMS error is 0.068369 for maxAngle, coeff1, 2 = 144.0 0.05 0.5499999999999999\n",
      "RMS error is 0.071041 for maxAngle, coeff1, 2 = 144.0 0.05 0.6\n",
      "RMS error is 0.075628 for maxAngle, coeff1, 2 = 144.0 0.05 0.6499999999999999\n",
      "RMS error is 0.079101 for maxAngle, coeff1, 2 = 144.0 0.1 0.4\n",
      "RMS error is 0.073397 for maxAngle, coeff1, 2 = 144.0 0.1 0.45000000000000007\n",
      "RMS error is 0.069218 for maxAngle, coeff1, 2 = 144.0 0.1 0.5\n",
      "RMS error is 0.072193 for maxAngle, coeff1, 2 = 144.0 0.1 0.55\n",
      "RMS error is 0.076937 for maxAngle, coeff1, 2 = 144.0 0.1 0.6\n",
      "RMS error is 0.079446 for maxAngle, coeff1, 2 = 144.0 0.15 0.35\n",
      "RMS error is 0.074029 for maxAngle, coeff1, 2 = 144.0 0.15 0.4\n",
      "RMS error is 0.070189 for maxAngle, coeff1, 2 = 144.0 0.15 0.44999999999999996\n",
      "RMS error is 0.073457 for maxAngle, coeff1, 2 = 144.0 0.15 0.5\n",
      "RMS error is 0.078342 for maxAngle, coeff1, 2 = 144.0 0.15 0.5499999999999999\n",
      "RMS error is 0.079897 for maxAngle, coeff1, 2 = 144.0 0.2 0.3\n",
      "RMS error is 0.074776 for maxAngle, coeff1, 2 = 144.0 0.2 0.35000000000000003\n",
      "RMS error is 0.071277 for maxAngle, coeff1, 2 = 144.0 0.2 0.39999999999999997\n",
      "RMS error is 0.074829 for maxAngle, coeff1, 2 = 144.0 0.2 0.45\n",
      "RMS error is 0.079842 for maxAngle, coeff1, 2 = 144.0 0.2 0.49999999999999994\n",
      "RMS error is 0.080455 for maxAngle, coeff1, 2 = 144.0 0.25 0.25\n",
      "RMS error is 0.075636 for maxAngle, coeff1, 2 = 144.0 0.25 0.30000000000000004\n",
      "RMS error is 0.07248 for maxAngle, coeff1, 2 = 144.0 0.25 0.35\n",
      "RMS error is 0.076305 for maxAngle, coeff1, 2 = 144.0 0.25 0.4\n",
      "RMS error is 0.081426 for maxAngle, coeff1, 2 = 144.0 0.25 0.44999999999999996\n",
      "RMS error is 0.081118 for maxAngle, coeff1, 2 = 144.0 0.3 0.2\n",
      "RMS error is 0.076607 for maxAngle, coeff1, 2 = 144.0 0.3 0.25000000000000006\n",
      "RMS error is 0.073795 for maxAngle, coeff1, 2 = 144.0 0.3 0.3\n",
      "RMS error is 0.077883 for maxAngle, coeff1, 2 = 144.0 0.3 0.35000000000000003\n",
      "RMS error is 0.083097 for maxAngle, coeff1, 2 = 144.0 0.3 0.39999999999999997\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  \"HD1\" approach -- simply widen angles facing near-boundary edges\n",
    "\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.8*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [0,0.05,0.1,0.15,0.2,0.25,0.3]\n",
    "coef2 = [0.5,0.55,0.6,0.65,0.7]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c1 in range(len(coef1)):\n",
    "    for c2 in range(len(coef2)):\n",
    "        coeff1 = coef1[c1]\n",
    "        coeff2 = coef2[c2]-coeff1\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-2.*southArea)/3.  #this is the required area of each wedge except the south (shorted) wedge\n",
    "                northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(northDistance*tan(wHA), L+northDistance)\n",
    "                northPoint =     Point(0,                      L+northDistance)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2 =\",round(180./pi*maxAngle,2),coeff1,coeff2) \n",
    "        if(RMSE[c1][c2] < 0.07 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(coeff1)+\",\"+str(coeff2))\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "25a041c1-4756-430a-a6ca-b22900bd929d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.07873 for maxAngle, coeff1, 2 = 162.0 0 0.5\n",
      "RMS error is 0.072479 for maxAngle, coeff1, 2 = 162.0 0 0.55\n",
      "RMS error is 0.067643 for maxAngle, coeff1, 2 = 162.0 0 0.6\n",
      "RMS error is 0.064916 for maxAngle, coeff1, 2 = 162.0 0 0.65\n",
      "RMS error is 0.065122 for maxAngle, coeff1, 2 = 162.0 0 0.7\n",
      "RMS error is 0.078862 for maxAngle, coeff1, 2 = 162.0 0.05 0.45\n",
      "RMS error is 0.07288 for maxAngle, coeff1, 2 = 162.0 0.05 0.5\n",
      "RMS error is 0.068369 for maxAngle, coeff1, 2 = 162.0 0.05 0.5499999999999999\n",
      "RMS error is 0.066012 for maxAngle, coeff1, 2 = 162.0 0.05 0.6\n",
      "RMS error is 0.066594 for maxAngle, coeff1, 2 = 162.0 0.05 0.6499999999999999\n",
      "RMS error is 0.079101 for maxAngle, coeff1, 2 = 162.0 0.1 0.4\n",
      "RMS error is 0.073397 for maxAngle, coeff1, 2 = 162.0 0.1 0.45000000000000007\n",
      "RMS error is 0.069218 for maxAngle, coeff1, 2 = 162.0 0.1 0.5\n",
      "RMS error is 0.067232 for maxAngle, coeff1, 2 = 162.0 0.1 0.55\n",
      "RMS error is 0.068183 for maxAngle, coeff1, 2 = 162.0 0.1 0.6\n",
      "RMS error is 0.079446 for maxAngle, coeff1, 2 = 162.0 0.15 0.35\n",
      "RMS error is 0.074029 for maxAngle, coeff1, 2 = 162.0 0.15 0.4\n",
      "RMS error is 0.070189 for maxAngle, coeff1, 2 = 162.0 0.15 0.44999999999999996\n",
      "RMS error is 0.06857 for maxAngle, coeff1, 2 = 162.0 0.15 0.5\n",
      "RMS error is 0.069881 for maxAngle, coeff1, 2 = 162.0 0.15 0.5499999999999999\n",
      "RMS error is 0.079897 for maxAngle, coeff1, 2 = 162.0 0.2 0.3\n",
      "RMS error is 0.074776 for maxAngle, coeff1, 2 = 162.0 0.2 0.35000000000000003\n",
      "RMS error is 0.071277 for maxAngle, coeff1, 2 = 162.0 0.2 0.39999999999999997\n",
      "RMS error is 0.070024 for maxAngle, coeff1, 2 = 162.0 0.2 0.45\n",
      "RMS error is 0.071686 for maxAngle, coeff1, 2 = 162.0 0.2 0.49999999999999994\n",
      "RMS error is 0.080455 for maxAngle, coeff1, 2 = 162.0 0.25 0.25\n",
      "RMS error is 0.075636 for maxAngle, coeff1, 2 = 162.0 0.25 0.30000000000000004\n",
      "RMS error is 0.07248 for maxAngle, coeff1, 2 = 162.0 0.25 0.35\n",
      "RMS error is 0.071588 for maxAngle, coeff1, 2 = 162.0 0.25 0.4\n",
      "RMS error is 0.073591 for maxAngle, coeff1, 2 = 162.0 0.25 0.44999999999999996\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Repeat, but with alternate maxWideAngle\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [0,0.05,0.1,0.15,0.2,0.25]\n",
    "coef2 = [0.5,0.55,0.6,0.65,0.7]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c1 in range(len(coef1)):\n",
    "    for c2 in range(len(coef2)):\n",
    "        coeff1 = coef1[c1]\n",
    "        coeff2 = coef2[c2]-coeff1\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-2.*southArea)/3.  #this is the required area of each wedge except the south (shorted) wedge\n",
    "                northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(northDistance*tan(wHA), L+northDistance)\n",
    "                northPoint =     Point(0,                      L+northDistance)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2 =\",round(180./pi*maxAngle,2),coeff1,coeff2) \n",
    "        if(RMSE[c1][c2] < 0.07 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(coeff1)+\",\"+str(coeff2))\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "c5a94be6-d067-450a-84e7-6b909d7b68db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.072522 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.05 0.6\n",
      "RMS error is 0.065215 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.05 0.65\n",
      "RMS error is 0.05895 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.05 0.7\n",
      "RMS error is 0.054544 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.05 0.75\n",
      "RMS error is 0.065133 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0 0.6\n",
      "RMS error is 0.059053 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0 0.65\n",
      "RMS error is 0.05489 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0 0.7\n",
      "RMS error is 0.053845 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0 0.75\n",
      "RMS error is 0.059207 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.05 0.6\n",
      "RMS error is 0.055292 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.05 0.65\n",
      "RMS error is 0.054529 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.05 0.7\n",
      "RMS error is 0.058202 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.05 0.75\n",
      "RMS error is 0.055747 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.1 0.6\n",
      "RMS error is 0.055264 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.1 0.65\n",
      "RMS error is 0.059198 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.1 0.7\n",
      "RMS error is 0.070371 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.1 0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, try a cubic function\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [-0.05,0,0.05,0.1]\n",
    "coef2 = [0.6,0.65,0.7,0.75]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c1 in range(len(coef1)):\n",
    "    for c2 in range(len(coef2)):\n",
    "        coeff1 = 0.\n",
    "        coeff2 = coef1[c1]\n",
    "        coeff3 = coef2[c2]-coeff1\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio + coeff3 * ratio**3))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-2.*southArea)/3.  #this is the required area of each wedge except the south (shorted) wedge\n",
    "                northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(northDistance*tan(wHA), L+northDistance)\n",
    "                northPoint =     Point(0,                      L+northDistance)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2, 3 =\",round(180./pi*maxAngle,2),coeff1,coeff2,coeff3) \n",
    "        if(RMSE[c1][c2] < 0.06 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(coeff1)+\",\"+str(round(coeff2,3))+\",\"+str(round(coeff3,3)))\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "6f68befb-c980-4425-a5ee-6ecabedbd831",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L, ratio, wideAngle are 0.005 0.999975 153.0\n",
      "L, ratio, wideAngle are 0.015 0.999775 152.96\n",
      "L, ratio, wideAngle are 0.025 0.999375 152.88\n",
      "L, ratio, wideAngle are 0.035 0.998775 152.77\n",
      "L, ratio, wideAngle are 0.045 0.997975 152.62\n",
      "L, ratio, wideAngle are 0.055 0.996975 152.43\n",
      "L, ratio, wideAngle are 0.065 0.995775 152.2\n",
      "L, ratio, wideAngle are 0.075 0.994375 151.94\n",
      "L, ratio, wideAngle are 0.085 0.992775 151.64\n",
      "L, ratio, wideAngle are 0.095 0.990975 151.31\n",
      "L, ratio, wideAngle are 0.105 0.988975 150.94\n",
      "L, ratio, wideAngle are 0.115 0.986775 150.53\n",
      "L, ratio, wideAngle are 0.125 0.984375 150.09\n",
      "L, ratio, wideAngle are 0.135 0.981775 149.62\n",
      "L, ratio, wideAngle are 0.145 0.978975 149.11\n",
      "L, ratio, wideAngle are 0.155 0.975975 148.57\n",
      "L, ratio, wideAngle are 0.165 0.972775 147.99\n",
      "L, ratio, wideAngle are 0.17500000000000002 0.969375 147.39\n",
      "L, ratio, wideAngle are 0.185 0.965775 146.75\n",
      "L, ratio, wideAngle are 0.195 0.961975 146.08\n",
      "L, ratio, wideAngle are 0.20500000000000002 0.957975 145.39\n",
      "L, ratio, wideAngle are 0.215 0.953775 144.66\n",
      "L, ratio, wideAngle are 0.225 0.949375 143.91\n",
      "L, ratio, wideAngle are 0.23500000000000001 0.944775 143.13\n",
      "L, ratio, wideAngle are 0.245 0.939975 142.32\n",
      "L, ratio, wideAngle are 0.255 0.934975 141.49\n",
      "L, ratio, wideAngle are 0.265 0.929775 140.64\n",
      "L, ratio, wideAngle are 0.275 0.924375 139.76\n",
      "L, ratio, wideAngle are 0.28500000000000003 0.918775 138.86\n",
      "L, ratio, wideAngle are 0.295 0.912975 137.94\n",
      "L, ratio, wideAngle are 0.305 0.906975 137.0\n",
      "L, ratio, wideAngle are 0.315 0.900775 136.05\n",
      "RMS error is 0.05489 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0.0 0.7\n",
      "L, ratio, wideAngle are 0.005 0.999975 152.99\n",
      "L, ratio, wideAngle are 0.015 0.999775 152.95\n",
      "L, ratio, wideAngle are 0.025 0.999375 152.87\n",
      "L, ratio, wideAngle are 0.035 0.998775 152.74\n",
      "L, ratio, wideAngle are 0.045 0.997975 152.56\n",
      "L, ratio, wideAngle are 0.055 0.996975 152.35\n",
      "L, ratio, wideAngle are 0.065 0.995775 152.09\n",
      "L, ratio, wideAngle are 0.075 0.994375 151.79\n",
      "L, ratio, wideAngle are 0.085 0.992775 151.45\n",
      "L, ratio, wideAngle are 0.095 0.990975 151.07\n",
      "L, ratio, wideAngle are 0.105 0.988975 150.65\n",
      "L, ratio, wideAngle are 0.115 0.986775 150.19\n",
      "L, ratio, wideAngle are 0.125 0.984375 149.68\n",
      "L, ratio, wideAngle are 0.135 0.981775 149.14\n",
      "L, ratio, wideAngle are 0.145 0.978975 148.57\n",
      "L, ratio, wideAngle are 0.155 0.975975 147.95\n",
      "L, ratio, wideAngle are 0.165 0.972775 147.3\n",
      "L, ratio, wideAngle are 0.17500000000000002 0.969375 146.61\n",
      "L, ratio, wideAngle are 0.185 0.965775 145.89\n",
      "L, ratio, wideAngle are 0.195 0.961975 145.13\n",
      "L, ratio, wideAngle are 0.20500000000000002 0.957975 144.35\n",
      "L, ratio, wideAngle are 0.215 0.953775 143.53\n",
      "L, ratio, wideAngle are 0.225 0.949375 142.68\n",
      "L, ratio, wideAngle are 0.23500000000000001 0.944775 141.8\n",
      "L, ratio, wideAngle are 0.245 0.939975 140.89\n",
      "L, ratio, wideAngle are 0.255 0.934975 139.96\n",
      "L, ratio, wideAngle are 0.265 0.929775 139.0\n",
      "L, ratio, wideAngle are 0.275 0.924375 138.02\n",
      "L, ratio, wideAngle are 0.28500000000000003 0.918775 137.01\n",
      "L, ratio, wideAngle are 0.295 0.912975 135.98\n",
      "L, ratio, wideAngle are 0.305 0.906975 134.94\n",
      "L, ratio, wideAngle are 0.315 0.900775 133.87\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_57/3597408155.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     70\u001b[0m             \u001b[0;31m#print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     71\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0myy\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mySlices\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 72\u001b[0;31m                 \u001b[0myUse\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0myy\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m0.5\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0myLayer\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0myy\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintersection\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfinalPoly\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marea\u001b[0m  \u001b[0;31m#0.5 is for normalization (half area was two)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     73\u001b[0m         \u001b[0mvariance\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     74\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0myy\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mySlices\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m#this loop: sum up the RMSE deviation from target\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/lib/python3.9/site-packages/shapely/geometry/base.py\u001b[0m in \u001b[0;36mintersection\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    687\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mintersection\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    688\u001b[0m         \u001b[0;34m\"\"\"Returns the intersection of the geometries\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 689\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mgeom_factory\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimpl\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'intersection'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    690\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    691\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0msymmetric_difference\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/lib/python3.9/site-packages/shapely/topology.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, this, other, *args)\u001b[0m\n\u001b[1;32m     66\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_validate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     67\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_validate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstop_prepared\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 68\u001b[0;31m         \u001b[0mproduct\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_geom\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_geom\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     69\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mproduct\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     70\u001b[0m             err = TopologicalError(\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    },
    {
     "data": {
      "image/png": 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r+gH8dHw8d7yyk60Hi6lrKORoSSVJvUOYMbwX/SOCMcZY9g63sraBBpthS04hnx4o4lBhBfvyywAID/anZ7cAbhjakyVTBtM1wLfT37tmwuBI5l7Rm5c+zWPqsGiXOndeXT59h95s1dZDPLEhm+fnj2TmcL2xUWsNjTYajeGZDw6wZnc+Z6rq8BJhQGQwdQ02XvnhaKrqGkno5bwrEusbbazenU+/sCCe+eAA/cKC2JB+kpr6ptvKhnXxo09oEDcnR9O7RyAJ0SF6L5M2lFXVc+OznxLWxY91d1+Dn497nIKpmuiQSzvyiiqY+tw2rhsUwcvfv6JTjKdersLyGp7amE3OqXIOnC6nvrHpNL/bU/oQ5OdDUu9uxIcHc6SkkolDIsk6Wc6YuLbPGKmqa8DHy4ttB4sYNyCc7bnFJPTqxue5JVTXN3K0pJLNWYUYYzhSUgVAgK8XNfU2Rsf2YMLgSJJ7hzCuf7jLDgW5mg8yT7Hgf3fzq5sG8YsbBlodR10EHXL5FjabYcmaNPx9vHjslmFa5naK7BrA7/9rBABv7DrOxoyTBPp58+bufHy9hZrt/38yhq4BPpTXNHBVfCiHiysZExdGaWUttfU2Any92X6omPjwLhwqqiSsix8llXXf2Ja3lzA2Pozq+kbuHBfHkZJKZo+MITzYn8iu/m5zkY8rmZQYxYzhvfjjxweZnBjF4Chr7z2jHKPTv0P/++dHeGhdJr+7bThzr+htdRy312gzCLD72BkOFVZQcLaatV+dYEhUNz7KPs3Y+DAOnC6nd48gfLyEE2erSYoJYUtOETNH9OL9jFP85No4GhoN1w2OoG9oED2C/HRYwAlKKmqZ9OxWevcIZM3PrtZfjG5Ch1wu4HhpFZP/sJXRsaG8eudofXfuRMYYSirrCL/AXR3rG234enthsxkdNulA69MKuPvfX/HA1CH89Dr3Oi21s/q2Qu+0v5KNMdy/Ng0vEZ6Yk6Rl7mQicsEyB76e9EHLvGNNT4pmcmJPnvnwAIeKKqyOoy5Tpy3013cdZ3tuCQ9MG0JM90Cr4yhlCRHht7OGEejrzeLVaTTaXP4mqOpbdMpCLzhbzePvZTE2Poz5o93jvuxKOUtktwAevDmB3UfP8I8dR6yOoy5Dpyt0YwzL3kqn0WZ4+tZk/RNfKWDOqBgmDI5g+fs5HGs+NVS5n05X6G99dYJPcopYPEUn0FXqP0SEJ2Yn4e0lLFmThlUnS6jL06kKvbC8hkfe3U9Kvx78YGys1XGUcim9ugeydNpQduSV8NrO4+3/gHI5nabQjTH85u0MqusbeXquDrUo1Zb5Y/owbkAYT2zIouBstdVx1EXqNIW+If0UmzJP86ubBtE/ItjqOEq5JBHhqTnJNNoMS99K16EXN9MpCr2kopYH38kguXcIP7kmzuo4Srm0PqFBLJkymC05RazZc8LqOOoidIpCf+Td/ZyrqWfF3OF6ebNSdrhjbCwp/Xrw6LuZFJ6rsTqOspPHt9sHmadYt6+An08cqDcgUspOXl7C8rnJ1DbYWPZ2hg69uAmPLvSyqnp+/XYGQ6O7ud30aUpZLT4imF/dNIgP959mfdpJq+MoO3h0oT/23n5KKutYMTf563uFKKXs9+Nr4hjeO4SH1mVSUlFrdRzVDo9tuU8PFPHm7nwWXhev02wpdYl8vL1YPnc45TX1PPzufqvjqHbYVegiMkVEckQkV0Tub2N5DxF5S0TSRGSniAxzfFT7ldfU88CaNAZEBvPziTobi1KXY3BUV34xcSDv7itgU+Ypq+Oob9FuoYuIN/ACMBVIAOaLSEKr1ZYCe40xycAdwHOODnoxnn4/m5Pnalg+N5kAX28royjlERZO6E9CdDd+/XYGZVX1VsdRF2DPO/QxQK4xJs8YUwe8DsxqtU4C8BGAMSYbiBWRng5NaqfPDxXzzy+O8eNxcYzq28OKCEp5HF9vL5bPTaa0so5H1+vQi6uyp9BjgJY3dshvfq6lfcAcABEZA/QDzpvPTUQWiEiqiKQWFRVdWuJvUVXXwP1r0okNC+J/Jg12+Osr1ZkNiwnhZ9f1Z82efD7JKbQ6jmqDPYXe1k1PWp+U+hTQQ0T2Aj8HvgIazvshY1YZY1KMMSkREREXm7Vdv9t0gGOlVTx9azKBfjrUopSj/fyGAQyIDGbp2nTKa3ToxdXYU+j5QJ8Wj3sDBS1XMMacM8bcaYwZQdMYegRw2FEh7bH7aCl/+/wwd4ztx5XxYR25aaU6DX8fb1bMTeb0uRqe3JhtdRzVij2FvgsYKCJxIuIHzAPWtVxBRLo3LwP4CbDVGHPOsVEvrKa+kUWr0+gVEsjiKUM6arNKdUoj+/bgx9fE8e8vj/F5brHVcVQL7Ra6MaYBuBvYBGQBbxhjMkVkoYgsbF5tKJApItk0nQ1zj7MCt+W5jw6SV1TJU7cmEezv05GbVqpT+p9Jg4kL78KStWlU1Z03uqosYtd56MaYDcaYQcaY/saYx5ufe8kY81Lz9zuMMQONMUOMMXOMMWecGbqltPyzrNqax+0pfbh2oOPH5ZVS5wvw9ebpW5M5XlrNik05VsdRzdz6StG6BhuLV6cRHuzH0ulDrY6jVKcyJi6UH4ztx6ufHyH1SKnVcRRuXugvfJJL9qlynpidREigr9VxlOp0Fk8Z0vTZ1eo0auobrY7T6bltoWedPMcLn+Qye2QMNwy15BompTq9Lv4+PH1rMnnFlTy7+YDVcTo9tyz0hkYbi1bvo3uQLw/e3PouBEqpjnTNwHDmje7Dn7fmse/4WavjdGpuWeirtuWRceIcv501jB5d/Nr/AaWUUy2dPpTIrgEsWr2P2gYderGK2xV6bmE5f9h8kGlJUUxNirY6jlIK6BbgyxNzhnHgdAUvfHLI6jidltsV+qmyWvr0COSRmZbeoVcp1crEIT2ZMzKGFz/JZX9Bh11XqFpwu0K/ZmA4H957HRFd/a2OopRq5cEZCXQP8mPR6n3UN9qsjtPpuF2hQ9MEtkop19M9yI/Hbkkks+Acq7bmWR2n03HLQldKua4pw6KZnhTNc5sPcvB0udVxOhUtdKWUwz08M5Eu/t4sWp1Go6313baVs2ihK6UcLqKrPw/PTGTv8bP8bXuH3km7U9NCV0o5xczhvbhxaCQrNuVwuLjS6jidgha6UsopRITHZyfh5+PFkjVp2HToxem00JVSTtOzWwC/uTmBnYdL+deXR62O4/G00JVSTnXbFb25dmA4T27M5nhpldVxPJoWulLKqUSEJ+ckIcDSt9IxRodenEULXSnldL17BHH/tKFsO1jMG6nHrY7jsbTQlVId4rtj+nJlXCiPrc/iVFmN1XE8kha6UqpDeHkJT9+aTL3NxjIdenEKLXSlVIeJDe/CfZMG81F2Ie/sLbA6jsfRQldKdag7x8Uxqm93Hn43k6LyWqvjeBS7Cl1EpohIjojkisj9bSwPEZF3RWSfiGSKyJ2Oj6qU8gTeXsLyucOpqmvkoXUZVsfxKO0Wuoh4Ay8AU4EEYL6ItJ7I8y5gvzFmODABeEZEdG44pVSbBkQG88sbB7Ih/RQb0k9aHcdj2PMOfQyQa4zJM8bUAa8Ds1qtY4CuIiJAMFAKNDg0qVLKoyy4Np6kmBAefCeD0so6q+N4BHsKPQZoeeJofvNzLa0EhgIFQDpwjzHmvOlKRGSBiKSKSGpRUdElRlZKeQIfby+Wz03mbFU9j76baXUcj2BPobc1PVDr840mA3uBXsAIYKWIdDvvh4xZZYxJMcakREREXGRUpZSnGRrdjbuuH8DbewvYvP+01XHcnj2Fng/0afG4N03vxFu6E1hrmuQCh4EhjomolPJkd10/gME9u7Ls7XTKquutjuPW7Cn0XcBAEYlr/qBzHrCu1TrHgBsARKQnMBjQCQWVUu3y8/FixW3JFFfU8cR7WVbHcWvtFroxpgG4G9gEZAFvGGMyRWShiCxsXu23wNUikg58BCwxxhQ7K7RSyrMk9+7OgvHx/N/U42w7qJ+vXSqx6vLblJQUk5qaasm2lVKup6a+kWnPb6O23same8cT7O9jdSSXJCK7jTEpbS3TK0WVUi4hwNebFXOTKSirZvn72VbHcUta6Eopl3FFv1DuvDqOf+w4yhd5JVbHcTta6Eopl3Lf5EH0DQ1iyZo0qusarY7jVrTQlVIuJcjPh6duTeJoSRXPfJBjdRy3ooWulHI5V/cP57tX9uWv2w+z59gZq+O4DS10pZRLemDaUHqFBLJ4dRo19Tr0Yg8tdKWUSwr29+GJOUnkFlbwx48PWh3HLWihK6Vc1nWDIrjtit689GkeGSfKrI7j8rTQlVIu7dfTEwjr4sd9b+6jruG8m7iqFrTQlVIuLSTIl8dnJ5F9qpw/bTlkdRyXpoWulHJ5NyX0ZObwXqz85CDZp85ZHcdlaaErpdzCwzMT6Rbgy+LVaTQ06tBLW7TQlVJuIbSLH4/MSiQtv4y/fHbY6jguSQtdKeU2pidFMyUxit9/eIBDRRVWx3E5WuhKKbchIjx6SyKBvt4sXp1Go82a23+7Ki10pZRbiewawEMzEth99Az/2HHE6jguRQtdKeV2Zo+M4frBESx/P4djJVVWx3EZWuhKKbcjIjwxJwkfL2HJmjRsOvQCaKErpdxUdEggS6cPZUdeCa/tOmZ1HJegha6UclvzRvdh3IAwntyQzYmz1VbHsZwWulLKbYkIT81JxmYMS9emY9Wk965CC10p5db6hAaxZMoQPj1QxJo9J6yOYym7Cl1EpohIjojkisj9bSxfJCJ7m78yRKRRREIdH1cppc73/av6MTq2B4++m0nhuRqr41im3UIXEW/gBWAqkADMF5GElusYY1YYY0YYY0YADwCfGmNKnZBXKaXO4+UlPH1rMrUNNpa9ndFph17seYc+Bsg1xuQZY+qA14FZ37L+fOA1R4RTSil7xUcE8z+TBvHh/tOsTztpdRxL2FPoMcDxFo/zm587j4gEAVOANRdYvkBEUkUktaio6GKzKqXUt/rxNfEM79Odh9ZlUlJRa3WcDmdPoUsbz13o75kZwPYLDbcYY1YZY1KMMSkRERH2ZlRKKbt4ewkr5iZTXlPPQ+syrY7T4ewp9HygT4vHvYGCC6w7Dx1uUUpZaFDPrvxi4kDWp53k/YxTVsfpUPYU+i5goIjEiYgfTaW9rvVKIhICXAe849iISil1cRZO6E9CdDd+804GZ6vqrI7TYdotdGNMA3A3sAnIAt4wxmSKyEIRWdhi1dnAB8aYSudEVUop+/h6e7HitmTOVNbx2/VZVsfpMD72rGSM2QBsaPXcS60evwq86qhgSil1ORJ7hfCzCf3548e53Dw8musHR1odyen0SlGllMe6e+IABkYGs3RtOuU19VbHcTotdKWUx/L38Wb53GROn6vhyY3ZVsdxOi10pZRHG9m3Bz+5Np5/f3mMz3OLrY7jVFroSimP96ubBhEX3oUla9OorG2wOo7TaKErpTxegG/T0Ev+mWpWbMqxOo7TaKErpTqF0bGh/GBsLH/fcYRdRzzz3oFa6EqpTmPR5MHEdA9kyeo0auobrY7jcFroSqlOo4u/D0/fmkxecSXPbj5gdRyH00JXSnUq4waEM39MH/68NY99x89aHcehtNCVUp3OA9OGEtk1gEWr91Hb4DlDL1roSqlOp1uAL0/MGcaB0xW88HGu1XEcRgtdKdUpTRzSkzkjY3hxyyEyC8qsjuMQWuhKqU7rwRkJdA/yY/HqNOobbVbHuWxa6EqpTqt7kB+P3TKMzIJzrNqaZ3Wcy6aFrpTq1KYMi2J6cjTPbT7IwdPlVse5LFroSqlO75GZiXTx92bR6jQabReaMtn1aaErpTq98GB/Hp6ZyN7jZ/nb9sNWx7lkWuhKKQXMHN6LG4f2ZMWmHA4Xu+dMmlroSikFiAiPzx6Gn48XS9akYXPDoRctdKWUatazWwC/uTmBnYdL+eeXR62Oc9G00JVSqoXbrujN+EERPLUxm+OlVVbHuSha6Eop1YKI8OScJAR4YG06xrjP0ItdhS4iU0QkR0RyReT+C6wzQUT2ikimiHzq2JhKKdVxYroH8sC0oXyWW8wbqcetjmO3dgtdRLyBF4CpQAIwX0QSWq3THXgRmGmMSQRuc3xUpZTqON8Z05er4kN5bH0Wp8pqrI5jF3veoY8Bco0xecaYOuB1YFardb4DrDXGHAMwxhQ6NqZSSnUsLy/h6VuTqbfZWPaWewy92FPoMUDLvznym59raRDQQ0S2iMhuEbmjrRcSkQUikioiqUVFRZeWWCmlOki/sC4smjyEj7ILeWdvgdVx2mVPoUsbz7X+VeUDXAFMByYDvxGRQef9kDGrjDEpxpiUiIiIiw6rlFId7YdXxzKqb3cefjeTwnLXHnqxp9DzgT4tHvcGWv+qygfeN8ZUGmOKga3AcMdEVEop63h7CcvnDqeqrpGH3sm0Os63sqfQdwEDRSRORPyAecC6Vuu8A1wrIj4iEgRcCWQ5NqpSSlljQGQw9944iI0Zp9iQftLqOBfUbqEbYxqAu4FNNJX0G8aYTBFZKCILm9fJAt4H0oCdwF+MMRnOi62UUh3rv6+NIykmhAffyaC0ss7qOG0Sqz65TUlJMampqZZsWymlLkX2qXPM+ONnTE+K5g/zRlqSQUR2G2NS2lqmV4oqpZSdhkR1467rB/D23gI27z9tdZzzaKErpdRF+D8TBjAkqivL3k6nrLre6jjfoIWulFIXwc/HixVzh1NcUcfj7+23Os43aKErpdRFSuodwoLx8byRms/WA65zkaQWulJKXYJ7bhhI/4guPLA2nYraBqvjAFroSil1SQJ8vVk+dzgFZdU8vTHb6jiAFrpSSl2yK/r14Efj4vjfL47yRV6J1XG00JVS6nLcN2kw/cKCWLImjeq6RkuzaKErpdRlCPTz5qk5yRwtqeKZD3IszaKFrpRSl2ls/zC+d1Vf/rr9MHuOnbEshxa6Uko5wP1Th9IrJJBFb+6jpt6aoRctdKWUcoBgfx+enJPEoaJKnv/ooCUZtNCVUspBxg+K4L9SevPy1jzS88s6fPta6Eop5UDLpicQ1sWPRav3Uddg69Bta6ErpZQDhQT68vjsJLJPlfOnLYc6dNta6Eop5WA3JfRk1oherPzkINmnznXYdrXQlVLKCR6akUi3AF8Wr06jobFjhl600JVSyglCu/jx6KxhpOWX8ZfPDnfINrXQlVLKSaYlRTElMYrff3iA3MIKp29PC10ppZxERHj0lkSC/LxZvHofjTbnzuGsha6UUk4U2TWAh2YksOfYWf7++RGnbksLXSmlnOyWETFMHBLJ8k3ZHC2pdNp27Cp0EZkiIjkikisi97exfIKIlInI3uavBx0fVSml3JOI8PjsYfh6eXH/mnRsThp6abfQRcQbeAGYCiQA80UkoY1VtxljRjR/PergnEop5daiQwJZNn0oO/JKeG3XMadsw8eOdcYAucaYPAAReR2YBbjWdNdKKeXibh/dh88PlRAa5OeU17en0GOA4y0e5wNXtrHeWBHZBxQA9xljMluvICILgAUAffv2vfi0SinlxkSE5+ePdNrr2zOGLm0813oAaA/QzxgzHPgj8HZbL2SMWWWMSTHGpERERFxUUKWUUt/OnkLPB/q0eNybpnfhXzPGnDPGVDR/vwHwFZFwh6VUSinVLnsKfRcwUETiRMQPmAesa7mCiESJiDR/P6b5da2fAlsppTqRdsfQjTENInI3sAnwBl4xxmSKyMLm5S8Bc4GfiUgDUA3MM8Y495IopZRS3yBW9W5KSopJTU21ZNtKKeWuRGS3MSalrWV6pahSSnkILXSllPIQWuhKKeUhLBtDF5Ei4Ogl/ng4UOzAOFbSfXFNnrIvnrIfoPvyH/2MMW1eyGNZoV8OEUm90IcC7kb3xTV5yr54yn6A7os9dMhFKaU8hBa6Ukp5CHct9FVWB3Ag3RfX5Cn74in7Abov7XLLMXSllFLnc9d36EoppVrRQldKKQ/h0oVux1ymIiLPNy9PE5FRVuRsjyfNySoir4hIoYhkXGC5WxwTsGtf3OK4iEgfEflERLJEJFNE7mljHbc4Lnbui7sclwAR2Ski+5r35ZE21nHscTHGuOQXTXd2PATEA37APiCh1TrTgI00TcJxFfCl1bkvcT8mAOutzmrn/owHRgEZF1ju8sfkIvbFLY4LEA2Mav6+K3DAHf9fuYh9cZfjIkBw8/e+wJfAVc48Lq78Dv3ruUyNMXXAf+YybWkW8A/T5Augu4hEd3TQdtizH27DGLMVKP2WVdzhmAB27YtbMMacNMbsaf6+HMiiaerIltziuNi5L26h+d91RfND3+av1mehOPS4uHKhtzWXaesDa886VrM349jmP802ikhix0RzCnc4JhfDrY6LiMQCI2l6N9iS2x2Xb9kXcJPjIiLeIrIXKAQ+NMY49bjYM0m0VeyZy9Sedax2MXOyVojINJrmZB3o7GBO4g7HxF5udVxEJBhYA/zSGHOu9eI2fsRlj0s7++I2x8UY0wiMEJHuwFsiMswY0/IzG4ceF1d+h97uXKZ2rmO1zjYnqzscE7u403EREV+aCvBfxpi1baziNselvX1xp+PyH8aYs8AWYEqrRQ49Lq5c6O3OZdr8+I7mT4qvAsqMMSc7Omg7OtucrO5wTOziLselOeNfgSxjzO8vsJpbHBd79sWNjktE8ztzRCQQuBHIbrWaQ4+Lyw65GPvmMt1A06fEuUAVcKdVeS/Ezv1wmzlZReQ1ms4yCBeRfOAhmj7scZtj8h927Iu7HJdxwPeB9ObxWoClQF9wu+Niz764y3GJBv4uIt40/dJ5wxiz3pkdppf+K6WUh3DlIRellFIXQQtdKaU8hBa6Ukp5CC10pZTyEFroSinlIbTQlVLKQ2ihK6WUh/h/GUOMrtPBIFgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, play more with cubic function -- try very specific\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [0., 0., -0.05,-0.15]\n",
    "coef2 = [0.,-0.3,-0.05, -0.15]\n",
    "coef3 = [0.7, 1., 0.8, 1]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c in range(len(coef1)):\n",
    "    for dummy in range(1): #too lazy to indent\n",
    "        coeff1 = coef1[c]\n",
    "        coeff2 = coef2[c]\n",
    "        coeff3 = coef3[c]\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio + coeff3 * ratio**3))\n",
    "                if (ratio > 0.9):\n",
    "                    print(\"L, ratio, wideAngle are\",L, ratio, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-2.*southArea)/3.  #this is the required area of each wedge except the south (shorted) wedge\n",
    "                northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(northDistance*tan(wHA), L+northDistance)\n",
    "                northPoint =     Point(0,                      L+northDistance)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2, 3 =\",round(180./pi*maxAngle,2),coeff1,coeff2,coeff3) \n",
    "        if(RMSE[c1][c2] < 1000) :   #0.06 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(coeff1)+\",\"+str(round(coeff2,3))+\",\"+str(round(coeff3,3)))\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "9697ee8e-5197-4fad-8670-093eba451030",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.066179 for maxAngle, coeff1, 2, 3 = 144.0 0.0 0.0 0.7\n",
      "RMS error is 0.065166 for maxAngle, coeff1, 2, 3 = 144.0 0.0 -0.3 1.0\n",
      "RMS error is 0.065607 for maxAngle, coeff1, 2, 3 = 144.0 -0.05 -0.05 0.8\n",
      "RMS error is 0.066224 for maxAngle, coeff1, 2, 3 = 144.0 -0.15 -0.15 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, play more with cubic function -- try very specific\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.8*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [0., 0., -0.05,-0.15]\n",
    "coef2 = [0.,-0.3,-0.05, -0.15]\n",
    "coef3 = [0.7, 1., 0.8, 1]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c in range(len(coef1)):\n",
    "    for dummy in range(1): #too lazy to indent\n",
    "        coeff1 = coef1[c]\n",
    "        coeff2 = coef2[c]\n",
    "        coeff3 = coef3[c]\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio + coeff3 * ratio**3))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-2.*southArea)/3.  #this is the required area of each wedge except the south (shorted) wedge\n",
    "                northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(northDistance*tan(wHA), L+northDistance)\n",
    "                northPoint =     Point(0,                      L+northDistance)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2, 3 =\",round(180./pi*maxAngle,2),coeff1,coeff2,coeff3) \n",
    "        if(RMSE[c1][c2] < 1000) :   #0.06 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(coeff1)+\",\"+str(round(coeff2,3))+\",\"+str(round(coeff3,3)))\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "f0d1f70b-a24d-47d4-bf54-281467cc9635",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.04201 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.2 0.6\n",
      "RMS error is 0.03897 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.2 0.65\n",
      "RMS error is 0.038235 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.2 0.7\n",
      "RMS error is 0.039375 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.15 0.6\n",
      "RMS error is 0.038925 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.15 0.65\n",
      "RMS error is 0.041197 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.15 0.7\n",
      "RMS error is 0.039643 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.1 0.6\n",
      "RMS error is 0.042144 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.1 0.65\n",
      "RMS error is 0.04729 for maxAngle, coeff1, 2, 3 = 162.0 0.0 -0.1 0.7\n",
      "RMS error is 0.049516 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0 0.6\n",
      "RMS error is 0.057198 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0 0.65\n",
      "RMS error is 0.066935 for maxAngle, coeff1, 2, 3 = 162.0 0.0 0 0.7\n"
     ]
    },
    {
     "data": {
      "image/png": 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9EyPJ2ynnoEZr/QXG2fo81/djC9U7EK7KMoyrHedgtCEoxDjDRWu9AyNhz8bYNkYAV2itba7634aRrA+7nc1dD6CUinENx7imtQTjXv5yjCt1e4F/VRXc8eaXlRcyZrIdaK61zql+3UVtUUp1wdhI/bXW9jOclgY6uC6fClFjlPHj1Ula639UMH4FRuOnCp9OcwrzugHjsvKjZzotT6KMH/DO1lq3qbJwA1HlvRXX6eH9GK2MJGmZSCl1FcZZTzDGUdbXZ5q0hKgvtNbVvkzryZTRuGMIxllPM4wzkC9MDcrDVHqpUBk3inMwfsdT5embqHW3YVxz34lx2eAOc8MRQtQChXGJ/hjGpcJtVH5Pu8Gp1qVCIYQQwlPIswqFEEJ4FW9+ACcAkZGRum3btmaHIYQQXmX9+vXpWuvKfszvsbw+cbVt25Z169aZHYYQQngVpdSpPHHEo8ilQiGEEF5FEpcQQgivIolLCCGEV5HEJYQQwqtI4hJCCOFVJHEJIYTwKpK4hBBCeBWv/x2X+Ju9xIHWkJNeiNOuKcyz4ShxopTCXuIkqJEfjhIn4S2CcdidNIoMQJ3Qv58QQng+SVxebP+2TIoL7OzccJSSYgeHd2XjKHFiLymv8+YyFISE++N0aOJ6RKG1pvM5LVAomsU2qvrzQghhEklcXiRtfy55mUVsWLqXghwbOelGn4O+/laCGvkRFRNKWNMgAkJ8CQ7zB12Cj58m8+AeivMzyT6QSkFWOsUFRRTlHyPvkA8lxblsSG2Eduby5+JItDOfkLAYnPZcul8wCEdhDv1GXo6tqJBGkV75dBghRD3j9U+H79Onj67Pj3xylDj58/u9ZB7MJ3ndUQACG/nRrG0jWrRrTMsOYYRGBBDc2J/8rGPkZx1jy9JvyDl8iANJ2ymyl5wwPavDOBsLLLFTYrUQaLNT5OuDr1OR7+eDFR9KLCUYxzQndvXVJCyc4pICzhp7A5kl2Zw/dCxFuphGfnKGJoS3UUqt11r3MTuO0yGJy0PlZxezcm4Saftyyc0swj/Yh/a9m9G+d1Mio0MICPYFwGG3s3bhp2Tu3U3S+j9waA1aE1DiILCkhKj8Avyw0zIwB6tVEdXCnwytSW8bxaG8XP6K8EVnFZDYyE50piYjQNP2iAWHNZTWGTFoazO0CkajcZSkoACtC11R2tBKk9I9lEMhNgacdQn5jmIm9RxJgK8vzYKayT00ITyUJC4T1bfElXW0gJ8+2Eba/jzQmuhO4XQ5pyVxvf6+TFeQk01G6j5+eu1ljmWm43A68bU7CCsoIqYomyb+hbTpGIhvy5YEDr6cHRYHycGN+TxlOSl5e8ixZ6BdZ1NOe6jxP78jKBtNfbuSb8+ic5NuHM07REKTWI5lrKOrvS2+STZ8bBGUFBegdRHW3F/Ruhibj3EW57AWkB9g5+ceOWSEOWjhl0CgNZjx3UfRtWkM7cLj8LHI1WkhPIEkLhPVl8SVk1HITx9s58iubKx+Fjr0aUbXga2IjA4pLXN0zy72b/6LVZ+8h8PpxK/EQYvsPFroHLq0LSKwWzyBwydQ0iSWjNAoXl33FlvSEtmTtx2UE+30wZ7fEaszhG6NBxHsF8S13c7FomBgxyiKS5yEB/tVGmdxoZ09m9LZt/kQSeuOobWNkPwV+BXv5whZrlIaC5ptrbPZGOsgP7QAFIRZOtI8sDXjuo/k4g4DJIkJYSJJXCby9sRVXGjnt89T2LUxDe3UdOzfnITB0YQ1CyotczBpOzt/W8WaxV8BEJZfRMf8DNo0LaTlyOFYu1+E6nwJO7N2sjltMzPW/Jcc+1G0VjgLW6NKmjMg8jJiw5szvn8PQvx9qkxQVdFac+xwAXs2p/P7FzvRGiJDsmmit5C2fTmFVgtZgQEA+Ppp9sS2Ynmr9ZT4OUE5UCjaBw3iothBXN5pINGNmp5RPEKIUyOJy0Temri01iSvPcKGZfs4diiftgmR9LsslohWf59hpe/fy9YflrB2ydcANM/Oo5c+RKuEcBrf9DDEnAOhzVi+bzmr9v/OgpRP0ThwloThlz+YTmHxPDBoGDFNgmjWKKDW6mIrsrNnczrLP9yO3eYkKjqQmBZ5FP3wAtn5RaQENgYgQjuJ6hLPu1FFHAmykW1dDYDV0YS2wb24ptMl3NjzolqLUwjxN0lcJvLGxGUrsvPbwp0krjxAcJg/g6/vRNvukaXjiwsK2PL9d/z8yftooGVWLv2sqbQc1JnA8c9BVBe0xcoXyV+yeNdyfj+y3Di7yu9Mv7DruKBdPDf071DnDSOcTs3ezel8/+5WSoodNG0TSny/cHxXPU/arj38UeSHVooQu52O7WI4OOAf7GwcxGe7/4O25oFy4K+b0ztiCK9f+iA+VrmUKERtkcRlIm9LXAd2HOO7NzZhK3LQa2gMZ1/d7oQEs2/zRr6cPo0Sh53I3AIGOPfTekgngm75L4S3RQOLdn7Nwh3fsSH9V5z2YCz5Z3Fzl3u4sEtLukc3Nq9yLk6nZs9f6Sx9ZwtOu6ZVp3D6XNyG4O2fcvD3X/khJQO71Uqg3U6XNi3oPGYixe27cPPXj5NlP0CJzx60VjSz9uWFIY/TvXkMfj6SxISoSZK4TOQtictR4mTdkj1s/GE/oU0CGHx9J1q0a1yatPKzjvHN9Cc5sCeF4CIbPbMP0eXcJjS65zVo1hWUYvXB1Xyc+Dk/H1yK0x6Cb8E53N/nbs7v3Izo8KAqIqh7tiI7KeuPsvzD7QB06NuMQWM7ovf8waGlX/HNL5ux+fgQYLfTs100Xa6bRKPufZm8+HWSsrZz0LESAH9HWx7r9wSD4roSERRsZpWEqDckcZnIGxKXo8TJ9+9tZeeGo8T2iGTQ2E7Gky0w7nVtXfkTv815m/ycHGLTs+jTNpdWDz0NHYeDjz+H8w/z4Zb5fLD9bbTTijXvPB7o/U+Gd2tJ01q8d1VTso4UsH31IdYv2QtA/xFx9Lm4LbYDyRz8Zi6Llq2mxMdKUEkJ5/RLoP2YWwhu25HZa77jj4N/sjZrPko5sdib80CvqQxtl0CLxuafWQrhzSRxmcjTE1fGgTy+fW0TuZlFnDuyPT0vjCkd57DbWfHmf9m48keCi2z0LTpIz1uHYh06BRq1BGD5vpVMXj4ZBzacuT0Y3/ERxvaJo3UTzzvDqozWml0b09jx+2F2/5VOVEwo/a+Io023CIr3J7P3yw/5buU6HBYLjWw2Lh03mubDRmMJCmFx0jp+2r2GxQffRlnsKHskD/V6los6JNA0VM7AhDgdkrhM5MmJK21fLt++vgm05oKb4mndpYnbuD18/q+HyS/Ip21mFue3OUrY5JdRXS81xhekMWHxnezN246jqDm9Au7kwSGD6RUTblJtaoa9xMHvX+1iz1/pFOTY6HVRDF3OaUlIuD85m/4g5YsPWZG4G60UzWyFjP7fh/hGGEn8131bWJqymi/2vgGWElRJU14c+Dpnt4klNODMmvcL0dBI4jKRpyau5LVH+P7dRAJC/bji3h5ERhtPqNBak/THr/w46yWcBYX0yjhEr6s7E3T3x2D1QWvN3O2f8tqGt8m2ZWHJGs79A27gprO7mFyjmpV3rIivXtlI1pECmrQM5tI7E2gUGQjA/q8+YseSRfyVWYCPw0FHPwfDP1yMsloBWL1/C4t2rOSb/W+DxY7F1oZPLn+Xzk2jsFrkEVNCVIckLhN5YuJKXneEH9/fRtO2oVx6ZwL+Qb6l41Z/9D6/fb2A4CIbg3QqnZ98HJUwGqw+FNoL+fevL/L1nvk4CqPpETSOOdeNxs+n/vb3uX9bJl//ZyNaQ/dBrThvbKfSceunTyFp4xYOYqV5UT7d49uQMP390vHf71zDwu3LWJX2GTj9CHLE8+3Y14kKkcuHQlRFEpeJPC1xbfxhH78uSKFZbCMuvSuBwBDjEpatsIClr84g6c+1tMzK5aLowzR5Yg6q7QAAkjKTuPG7iRQ4srDk/oPnBk3loq7NG8QZxNG9OWxZeYBtvx4ipmsEvYe3oWWHMAAc9hK+vXU0+3IKsCkr/UOdxI8cTfglN5V+/qNNi/l8x9ekFKxCF7cixr8/n499gkA/aUIvREUkcZnIkxLXtt8OsvzD7cT2jGLYpK5YrMaZkr2khC8ev5/9e3bRLi2TwYMa0fjxL8E3EK01C5O/4LnfZ1JgcxLjuJWZV1xFlxYNq9Wc0+Fk1fxkdv2ZhsPu5OLbu9OifRgWV+IuOHyQD+++mTyrD4G2Eq67fjiNLx6PCv77vuGTP89myd6vyNOpBNvO5bwWF/L8pdfIE+qFKIckLhN5SuL668f9/PJZMq06hXPJHd3xCzCO9nPSjrLgiSkcO5ZBz/TDnHfTWfiOmgn+IWitmfHHLD7c8RaOwmguanofL181rEHvaLPTCpj/7DpshXbaJkRyyR3dS5eHrbiIPYu/4NuPPwI0McV5XPnBfKxhzUs/79ROrv/yfrbk/IjWil4Bd3BTz4u5oHNbcyokhIeSxFWdGSn1LnAZcFRr3a2c8Qp4FbgEKABu0lpvqGq6npC4dv+VxuI3txCbEMmwW/4+0yrMzWHuP28jNzuLvukH6fvPq/C9choA2cXZ3LFsMpsz10Jub14Y9CzDu7Vo0EnruPzsYrasPMC6b/fQOr4JvYe1oVWnv1tT7lr8JRsXzmV3Tj4x+Tl06xxFlxkLwG3ZZRdnc/H868h17kPbg5nS/XWu7ZlAkFw+FAKQxFW9GSl1HpAHfFBB4roEuAcjcfUHXtVa969qumYnrpT1R1n2vy1ExYQy4p+98As0dozpqftY8PgDFBQUMDB3P32euh/VdzwoRY4th3Ff30lK7hZ8si7jjSvu5ew4eTq6O601q7/YyY7fD2O3ObjmoT6EtwgqTexaa76+Zzw7j2aA1lze2pe2E+/Dp+v5pdPIteXy/e6fmfbbUzidCmtxJxaO/A/tmoaZVCshPIckrurOTKm2wDcVJK43gRVa67mu4R3AYK31ocqmaWbiyjiYx+fPryeiVTBX3NcLX3+juXZBTjYf3TOJ4txczsvZS7dn/w9rv+sBSDmWwvXf3ky+PYvmxTfxxfh7CA3wrWw2DVpOeiGfPr0GW5GDzgOac/74LiecleYeOcycuydQbLESWVDAmOlT8e82+IRp/LJ/HbPWv0ti9ioshd05K2w4s0dej7+PtY5r43201nIVoJ6SxFXdmVWeuL4BntNa/+Ia/hF4WGt9UlZSSt0K3AoQExPTe+/evbUad3kyDubx1ct/opTi2kf7EBJuPHrp2OGDzH/knxTk5zGkYD89Xn4J1dHoqmN39m6u+3oSOcWFdLVM5o1rryAixL/OY/c2WUcK2PjjfhJXHqDHha1JGBxd+psvgMx9e/hzzlts3LKJFnm5JDSDbm8tA58Tl+3jK2ayaO97AHT1uYcHzrmGvrERdVoXb1Fsd7DsnVnsWr4Ri7Jg9bdw6SP30qZzd7NDEzVEEld1Z1Z54voWmF4mcT2ktV5f2TTNOOOyFdn5bLrRgOCqB84q7fTRVlTIh3dOID87m/Ny9pDw0nNYEkYA8PuBtdz+w+3Y7T6cE/wwb46+So5kT4HTqVny5mZ2/5VOSLg/Y57od8Lv4wB+mDaFzVu3ojVcFllMuzsfwNr94hPKFJQUcMn868iw78RZHMm/+7/G1T3i67IqHm1vWjZr5s/m8KoU7BTh1LkorGiK8bc24+5P3jE7RFFDvDlxedIvW1OB1m7D0cBBk2KpkMPuZNk7iWQdLWDoxK6lSasgJ5t5D95NVl4uZxccoMd/XylNWonpidz1w33YihtzRdRMZo28UpLWKbJYFJfckcA1D/UmP9vG5y+sZ8cfh08oc+G0Gdz21kf4o/k23Y/PHpqObeOyE8oE+Qax8Jp3ubXbvVj9svm/1Q9w/uwXSMstqsvqeJTiEjuLf1nBW/++n0X3TOHAqkRs+hBOfYzI6Pbc/+nn+Ps0o9hxlK9efcnscIXwqMS1CBinDAOA7Krub5nhl/nJ7N2cwaCxnYh2tXRzOh0smvoQGUcOMSA9lbOmPYLqPAyAlft/Y+y3N1BUYuGaVk/w7BXn1usnYdS25nGNuWB8F5RF8dOcbaTtyz1hfFBYONc+/x86dornQKNGfPfoNA5MvhDsxaVlmgQ04Z7et/Bo32kEBWWTFvgh1817me+3HsHbfx5yKvYeOcqMdx7lzSk3kjLrY/IT07Dpgzh0Js3adOfO/81l/EsvAnD+PRMAP/b8vokSm83cwEWDV5etCucCg4FI4AjwL8AXQGs929UcfhYwHKM5/ITy7m+VVZeXCnf9mcbiNzfT88LWnDuyAwDa6WTpy8+RuOY3emUeYvC027CceytgPA1jzNfjKSoK5sY2z/HwRb1Lf1ArzkxRfglzn/yDglwbXc5uwZAbO59wFqu1ZtGUu0jZvw8fh4NruwbR8p7nIbL9CdNxaidXL7yZnXnrcdoimNz1JSad07uuq1MnnE7N3swCNm39hY1LnyPscBPIb4SDIrTOAzTtegxk0M0TCG9+civX2RNvJT/vIGHN45j46n/qvgKiRnnzpUL5AXI1HdmTw5cvbaBJy2CufrA3Vl/jrGnFG6+yfsX3tE/PYPhdw/C/ehoAfx7ZyM1LbsFm9+XaltOZdvGgWo+xock6WsCGpXvZ9ush/nFtB7qe1xIf379bCmqnk4PbE1nwr4cJKLbTuTiDgW+/gyWm5wnTybXl8tmOz3l1/SzsRU2JViP4YMw4mjUOpD7YfTSXrzdsImv7AgK2rSMkO4Yi7GjsoJ2AkwGXjqXn5cMJDg+rcDq5xzL53x13o3Fy/YznaNa6bV1VQdQCSVwmqovEZSuy8+kza9EOzchH+hDUyHj+YMrvv/DVzOnEZOdwxTVx+E96DywW0grSuPTzkeQXwVXNn+WpS8+RM61a4nRqvpy5gUMp2UREh3Dtw31KDyqO2/79YlZ+8D9ybcUMLD5Mr/GXGj8EL3Ofcf62RTyzZipOHETbJzBj+ES6tfK+R2/lFJWQdDiXdcnrWb11HtEHd9JyTwQWHUaBOgIoLCoYlOLy+x4irm8CFmv1fhrw4WMPcXTnVgIDmnPnnP/VbkVErZLEZaLaTlxaa358fxs71hzmqvt70bKDcV9r/+a/WPD044QUFDOyjz/hTywCi4UDeQcY9dU4sm1ZXNBoGq9ec3mtxSYM9hIHSX8cYflH2+l8Tgv6Xx5b+vOE4xz2EuZMGE12URFNc/O56rZLCbrqoZOmVewo5qqFN7Evbwf2vE48/Y9pjOzV6aRynqTY7iCroITfdh5kybZtOA9/hSV3Le32hhOR1Zp8XyghA4CAgJb4+Poz6t9TCW8RdVrze3XsBOzOY5w77iYGXHplDdZE1CVJXCaq7cS1afl+Vn2aTL/LY+l7aSwAhXm5vH/bjZBfwIgmh2k5awUENcHmsHHpgjEcyt9PgvUh3r/+GmmIUYdWzt3B5p8PEBjqy3X/GkBAyInN5bOPHuH3Of9jy7rVdMjK4B9dnDSZvhQCw04od7TgKM//8QrL9n4L+d0YEH4zz1x+Lk1DT0yGZikqcVBgc/BrylHW70tj6/4l5BavoU3mblocdNDyWGeKfAIosRShdSEArdqfh39QEJdNuQ1fvzP7wfsPH73LX19/ia8lknvnvlsTVRImkMRlotpMXMcO5/PpM2tp3TmcS+5IQFkU9pISPnvoHg6l7meYM5Wu73wNYTEUO4qZtPheNmb8RjvnXXw+/rYG0SWJpzmyO4eFM9bTqlMYZ1/VnqiY0JPKLHr8fpJTkgiw2bmmmx/Np7wJjVqcVO6F32fx4Y430VoRnj+ef7Qcwr3nd6FFHd/7OpxdhM3u5PttB9iTkccf+1ZwrHgnLSwbsJbk0D8xhOiMJuQERVBoyQY04AtKcd519+AfEkTC+f1qNKZZN0ykuOQIrXv2Y9SjU2t02qJuSOIyUW0lLqfDyeczNpCdVsDYqf0Jbmw8hWHpC0+zZf3v9Ek/wMBZL2DpMhSAe79/jOUHvyY4dxTfTXiYJsHSlbxZ/vpxP79/uRMUjJ3a/4SnbAA47HaSflvJklkvEZlXwACfA7SfNRcVc2JrQq01G45u4KlfXmJX3ma0tuKXdSWNLbHcd975NArw45x2kQT41syjo9LzivG1Wli9Mx2bQ/NN4nZyimwkZf1KkT5GROAGSnzy6LPDTuxhC1HZcRT6BZHva0dj/A4tMKQDVquVsdOn4hvgR2Bw7Zwl7tryF18+/TQWArhzzv/w85cnwHgbSVwmqq3EtW7xHv74ahcXTepKhz7NAEhZ/QtfvfIccccyufyfV+BzySMAfJz4Gc+tewr/vAv4btxzHnNJqSHLzSzikyf/oEnzIM65uv0JT5c/7o8P3+OXbz7H4tQMte+nw/kd8b/5TQg+8TFQWUVZzN0xlx93/8aO7I0A2PM6op2+tGA4BSU2RnU/l6x8J5d0b8n+zALOaR9BytE8urdqTNKRPNo3DWFTahZxUSGs3plBq/BAVmw/QkSIP8uSEgnyDSLx2BqcTgWBf4HFjn/AbuyWEnru0kTmQN8djQko8edAeBTF1kKMMysrKF86nXstfgH+DJ00os5+3P7WbXeQm7Wf0CYx3PrG63UyT1FzJHGZqDYSV3pqHp9NX0tczyiG3dLN9d4+PnnwLgIKihg9MILGU+YBsGTXj0xZORlHQXvmXPImfdue3g1vUfOS1hzml8+SKc63M+r/+hLRMuSkMscOHWDeA3fiKCqmSV4hQ1ofIzy+NQET/guNosHn7zPnQnshi1IWcSDvCO8lvo0VHxzYAXAUNcPim01JTncsvsdwFnRC+R1GFcfh9NuHskWD/26ctiiswTtxloThE5yMdgRh9T8KaKxOB04L9NuhCSvWnLPZj2CbhX1hrSnytWCz2jGSlQX/4C5YfX0ZMeU+LAqat6v77a64oIA3br4VJzZGPjmVmE4nPclNeDBJXCaq6cTlsDv57Ll1FGQXM/Zf/QkM8cNhL+GD28aRdyyLy4MO0PZ/v0BAI47kH2H4ghEUF4UxfcAbjOgRW2NxiJpRmGvjk2l/4BfkQ7eBreg5tPVJZyQHtm9l5TtvcGjvboKLimlUaGNAYCqNQmyEj7sNS2go9LrRePqG615YZlEmTu3krb/eIjIwknc2v0/r0Bh2ZCXiZwnA5jz5EVIKhUYTgC/F2Omaocjzh8vWFRGMk2a7QrA6FXvCmlNitZDnrzASFShrJBZLIJ3/cSUBoQEMuu48j3hs2Lx//4sDW9YT4Necuz6U5vHeRBKXiWo6cf2xaBfrvtvDJXd0J7aHcRS7fNZMNqz6iXNzU+n/3ieoZvHk2nK5cuH1HCk8wKgWLzF1+OAai0HUrL2JGaz+YicZqXn0HBpDbI9IWrYPO6nctp+WseqT9ynIzcFid2B1OonPTAOHomtMJhSVED6sPyWp+wkcOgZ9YDOWhCvQ+9ZAuyGw+2eSI2OJ3rue3xqH0XnbBtY2i6Db6vXsbNmEuDUHyQlVqJQgfH3t7C2JwOLU7I00LmMW+h2/V2YBFYzFGkrjFv0IbtyYCyZcjI+vpfTZmJ7kP2NvpsSZwVlXj2TI6BvNDkdUkyQuE9Vk4jqyJ4fPX1hPx37NuPAm44nhyb+uZNF/XiAmK5urHrkenyG3o7Vm/Lf3sCF9Fe2d9/H5TROkBaGH007NYtfT5QH6XhZLZHQIsT0iTzpz2bd5I79++C4FWZlkZWcBEFJkw+ZjpU16FoW+vrQtziLTGUhcQCaHC0NpHZLFgbzGtAjKYV9+GE1989lDGI3txaSGNCKouIQD4aH42x1kBbkaMhyfrwpEqSCUNRLfoDhCI6I4a/g5hIT7EZvg+R2M/vrVfH7/5BN8LeHcO/c9s8MR1SSJy0Q1lbjsJQ7mP7MWW5GDsVONLjMKcrJ597Yb8c8v5Nq+/oT939egFB9s/pQZG54mtGAE3988jWB/6Q7eG2inJvNwPr/MTyZ1+zEA2iZEEtTYj36XxaKdEBL+d+u4ovw8dvy2EntRMX98PpegkFAy0o6UmagGpbA4nTgtFpRTo086iDEu+Vl9QtFOG1ijUSoA5dsKqzWc8JbNiO0RR2R0CHE9o1AWhdXLfv/32rhJFBUfpnmn7lz/1HSzwxHV4M2JS/a4Lmu+3s2xwwVcfk+P0n6evn/uSWx2B0OD0wmbsgKU4o+D63hx/XScBR14+8oHJGl5EWVRRLQM4bJ7enDsUD6Jqw6SuOogSsG2Xw6igS7ntKAwt4SEIdFkHy2g87lDyTxUwB2XXknW0XyyjyThGxjB7g0/E9g4mtTNvxLUpD0Zu//EL7QD+ZkpOFVbtDOdvKzmWCy5OJytQJfgFxiFU/sS3bEJ4S2CadkhjBbtGuMbYD3hGYve6OqnHmHuI49zNGk/+bm5BIee/Ps5IWqKnHEBGQfymP/MWjoNaM7547oAsGPFj3zzxst0OZbG8NdfxNJ+IHm2PC749Aryipw83ms21/XpXBNVECaylzg4uieHxF8OUlxgZ+/mDHx8LdhLnABYfBROuyY4zJ/8rGLCmwdx7HABjSIDyEkvwi/QB1uh/YRp+vpbKSl20DyuMU6Hk7heUfj6+9CqUxiNIgLx8bWg6uGl5f/dfTfZaXsIbtSK299+0+xwRBXkjMuLaa1ZOS8J30ArZ1/dDoDC3By+f/NVGhUWcd7VvbC0H4jWmnt/eJx8RzqDm0yTpFVP+PhaadkhnJYdwtFOTV6W0W9X8tojhEYEsOP3w0TFhJKy/ijx/2jJnk3pdDmnBfu3Z5JwfjRHdufQ7qymZB7Kp0PvpuRmFtGmWyROh5OQcH8sVu+65Hcmxs+cyWvjJlGQm8H29X/QuXd/s0MS9VSDT1xJfxzmYHIWg6/vRGCI8ZudZc89ic3hYGhwBiE3LwJg9p9zWJv2E8EFlzHjuivMDFnUEmVRhDYxfjx+1rA2AKU/Pu9/RZxpcXkLXz8/WveNZ8+aX/hh5lt0/lgSl6gdDedwsBzFBSX8+nkKzWIbEX9uSwB2rPyJlJQddMpKp8NTr4BfELuz9vDGpv+i8zvz0TWPEuTX4PO9EOW65oFH8LM2pdiexuJ33jA7HFFPNejE9cei3RTllTBobCeURVGYm8MPb7xCo8JiBl3VA0uHQdgcNm5ZMhmn08K9PR6lQ7NGZocthEc7++ZrAR+SflhjdiiinmqwiSttXy5bfk6l23mtSp8gvuz5pyh2OBgYlE7IxFcAmLpyBkeKU2jHRG45p5eJEQvhHfpceDGBgRHYnWm8/+D9Zocj6qEGmbiON8gICPGl/wjj3kXSyuWkJG+nU1Y6Hf/9CvgFse7wn3y791N88s/mvdE3e8QjdoTwBmOe/zcWFcqx1MNkZ6SbHY6oZxpk4lJKMXB0By4YH49/kC+2okJ+nP0KoYXFDLoyofQS4T9/fAynvRHPnPeIdFMixClo0qw5Ya2a49Q5fPLgY2aHI+qZBpm4AJq2aUSbbkb3Fb+8/goFDgfnBGYQMukVAJ7+9T9k21PpHXQLl3STFmVCnKobpj+Pj4qkoCCdjSu+NzscUY802MR1XPq+PWz8/RdisrPp8thT4BfM5rREvtj1IZb8vrw6YqzZIQrhlXz9/Gg/pDdQwqq355odjqhHGnTi0lqzbPq/sDqcDOwZgrXHZZQ4S7jn+0dxOoKZevbDhMslQiFO26W33YO/T1Ns9jS+fHWG2eGIeqJBJ66tyxZzKDOD7vlpNHt4NgAv/j6bjJLddPW7iWt6dTI5QiG83/n3TQT82Lt6CyU2m9nhiHqgwSYuW2EBP78/m0YFRZx90zBUeBt2ZCYzN+ldVH4PXrtyvNkhClEvxPc7h+CQSOw6gw8efMDscEQ90GAT18pZMyl0ODgn+BiBI6ficDq4e9kjOBx+TOn7CFGh/lVPRAhRLde/OB2Lakz20TSO7N9jdjjCyzXIxOV0Osn79WfaZGfT5fF/g48//13/LoeLk2hvvYEb+nQ1O0Qh6pXQ8CZEtotG6zwWPP602eEIL1dniUspNVwptUMplaKUeqSc8eFKqS+UUpuUUmuUUt1qKxaLUlx8UQTDh0Rg6X4Jh/IO8V7im1DQmTeunCg/NBaiFtz4zPP4WqIoKk5n9dcLzQ5HeLE6SVxKKSvwGnAxEA+MVUrFlyn2GLBRa50AjANercWA8L9zHiEPfArAgz8+g0M7mBT/AC3DgmpttkI0dF0vGwQ4WfvJN2aHIrxYXZ1x9QNStNa7tNY2YB4wokyZeOBHAK31dqCtUqpZrUblG8DP+35jU9bPNC4exl3/6FersxOiobvg+psI8I2ixHmU+c8+aXY4wkvVVeJqBex3G051vefuL+BqAKVUP6ANEF3exJRStyql1iml1qWlpZ12UCWOEh5b+RROWxNevOg+fBpQp39CmOXiR+5FqUAObkqhuKDA7HCEF6qrPXV5N410meHngHCl1EbgHuBPwF72QwBa67e01n201n2ioqJOO6hX1r5DjuMAvUMncHZci9OejhCi+uK69SCkcQQOfYw5DzxodjjCC9VV4koFWrsNRwMH3QtorXO01hO01j0x7nFFAbtrK6BDeYf4aPv/oKALMy+TxzoJUZfGvzwTqwon71g6e7dvMTsc4WXqKnGtBToopWKVUn7AGGCRewGlVJhrHMAkYKXWOqe2Avq7Qcb9RIbIb7aEqEv+QUE079YOrQv45plXzA5HeJk6SVxaaztwN7AU2AbM11onKqVuV0rd7irWBUhUSm3HaH14X23F43Q6OXi4FeHFI6RBhhAmGfN/0/CzNKXIlsbyuR+YHY7wIkrrsreavEufPn30unXrTvlzecV20nOLaRsZXAtRCSGq49dFC/j944/wtYRz79z3zA6nQVFKrdda9zE7jtPRYJvRhfj7SNISwmTnXjGSAP9ISpxpfPTESc8lEKJcDTZxCSE8w9VPPYpSwaQl7yc/N9fscIQXkMQlhDBVi7btaBQVhVNn8+FkeXq8qJokLiGE6ca/NBOrakJ+bibb1v5mdjjCw0niEkKYztfPj5h+XYEifnzlHbPDER5OEpcQwiNcff/D+FmbUmxP47u3XzM7HOHBJHEJITzGORNHAz4k/7TW7FCEB5PEJYTwGL0vGEZgUAR2ZzrvP3i/2eEIDyWJSwjhUcY8928sKpRjqYfJPHLY7HCEB5LEJYTwKE2aNSe8VXOcOodPH3nC7HCEB5LEJYTwODe+8CI+KpKCggw2/LjM7HCEh5HEJYTwOFarlQ7n9wHs/PrOp2aHIzyMJC4hhEe65Na78feJwuY4whcvP292OMKDSOISQnis8++bCPiz94+tlNhsZocjPIQkLiGEx4rvdw7BoRE4dAYfPCDN44VBEpcQwqPd+PJLWFRjstPSObRnp9nhCA8giUsI4dGCQ0OJah+N1nksnDrd7HCEB5DEJYTweDc8/Ty+liiKitNZ/fVCs8MRJpPEJYTwCl0vGwRo1n3yjdmhCJNJ4hJCeIULrr+JAL9IbM6jfPrMNLPDESaSxCWE8BqXPT4ZpQI5tHknxQUFZocjTCKJSwjhNdp07kZIWCQOfYw59z9gdjjCJJK4hBBeZfzMl7CqcPKy0tm1ZZPZ4QgTSOISQngV/6AgWnRvh9aFLH7uVbPDESaQxCWE8DqjH5+Gn6UpRSXp/Pjx+2aHI+qYJC4hhFfqc91lgCLxm5/NDkXUsTpLXEqp4UqpHUqpFKXUI+WMb6yU+lop9ZdSKlEpNaGuYhNCeJ+zL7+aAP9ISpxpfPj4w2aHI+pQnSQupZQVeA24GIgHxiql4ssUuwvYqrXuAQwGXlJK+dVFfEII73T1U4+iVAjpO1PJPZZpdjiijtTVGVc/IEVrvUtrbQPmASPKlNFAqFJKASFAJmCvo/iEEF6oRdt2NG4aiVNn8/GUky7kiHqqrhJXK2C/23Cq6z13s4AuwEFgM3Cf1tpZ3sSUUrcqpdYppdalpaXVRrxCCC8x7sWZWFUE+bkZbF3zm9nhiDpQV4lLlfOeLjM8DNgItAR6ArOUUo3Km5jW+i2tdR+tdZ+oqKiajFMI4WV8/fxo078rYOOnV98xOxxRB+oqcaUCrd2GozHOrNxNABZqQwqwG+hcR/EJIbzYVZMfws/alGJ7Gt+9NcvscEQtq6vEtRbooJSKdTW4GAMsKlNmH3ABgFKqGdAJ2FVH8QkhvNzAW8cAPiT/tI4Sm83scEQtqpPEpbW2A3cDS4FtwHytdaJS6nal1O2uYv8GzlFKbQZ+BB7WWqfXRXxCCO/Xc/BQgoIisOt0Pn5UmsfXZ0rrsreavEufPn30unXrzA5DCOEBMo8cZs599wOa8a++TJNmzc0OyWMppdZrrfuYHcfpkCdnCCHqjSbNmhPeujlOncu8h58wOxxRSyRxCSHqlZtmzMTHEklhYQbrf1xqdjiiFkjiEkLUOx0v6AfY+e2dT80ORdQCSVxCiHrn4kl34u8Thc1xlIUznzM7HFHDJHEJIeqlC++/FQhg35pt0jy+npHEJYSolzr37k9waAQOncGcB+43OxxRgyRxCSHqrRtffhGLakxOWhqH9uw0OxxRQyRxCSHqreDQUKI6tEbrfBZOnW52OKKGSOISQtRrN/z7OXwtURQVp/PrV5+ZHY6oAZK4hBD1XvcR5wOa9fMWmx2KqAGSuIQQ9d6QMTcS4BdFifMo8/79L7PDEWfIx+wAakNJSQmpqakUFRWZHYqoQEBAANHR0fj6+podimggLnv8n3w+7SkOJ+6iuKAA/6Ags0MSp6leJq7U1FRCQ0Np27YtSpXXh6Uwk9aajIwMUlNTiY2NNTsc0UC06dyNkPAIcjP38/7kB7jtzTfMDkmcpnp5qbCoqIiIiAhJWh5KKUVERIScEYs6N/6ll7CqcPKz09m15S+zwxGnqV4mLkCSloeT9SPM4B8URMuEDmhdyHfP/dfscMRpqreJSwghyjPqsan4WppSXHKUHz5+1+xwxGmQxFVLlixZQqdOnWjfvj3PPXfyQz611tx77720b9+ehIQENmzYUK3pTp8+nfbt29OpUyeWLi2/y4YpU6bQuXNnEhISuOqqq8jKyiq33Jw5c+jQoQMdOnRgzpw5Fc5z/vz5xMfH07VrV6677rrS961WKz179qRnz55cccUV1YpfCE/Q/4YrAAtbv1lldijidGitvfqvd+/euqytW7ee9F5dstvtOi4uTu/cuVMXFxfrhIQEnZiYeEKZb7/9Vg8fPlw7nU69evVq3a9fvyqnm5iYqBMSEnRRUZHetWuXjouL03a7/aRyS5cu1SUlJVprrR966CH90EMPnVQmIyNDx8bG6oyMDJ2ZmaljY2N1ZmbmSeWSkpJ0z549S8cdOXKkdFxwcHCVMVfG7PUkGrZZ4ybqF0ddqj94dIrZoZgCWKc9YB9+On/1slWhuye/TmTrwZwanWZ8y0b86/KuFY5fs2YN7du3Jy4uDoAxY8bw1VdfER8fX1rmq6++Yty4cSilGDBgAFlZWRw6dIgWLVpUON2vvvqKMWPG4O/vT2xsLO3bt2fNmjWcffbZJ5S76KKLSl8PGDCABQsWnDStpUuXMnToUJo0aQLA0KFDWbJkCWPHjj2h3Ntvv81dd91FeHg4AE2bNq0wPiG8ycin/4+PpzxC+q4D5B7LJDS8idkhiWqSS4W14MCBA7Ru3bp0ODo6mgMHDpxymdOZblnvvvsuF1988WlPKykpiaSkJM4991wGDBjAkiVLSscVFRXRp08fBgwYwJdffllpHEJ4mmat29K4WRROnc3HDz5qdjjiFNT7M67Kzoxqi3EWfqKyreiqU+Z0puvumWeewcfHh+uvv/60p2W320lOTmbFihWkpqYycOBAtmzZQlhYGPv27aNly5bs2rWL888/n+7du9OuXbtK6yCEJxk34yVeH38L+XnpbP19JfEDzjM7JFENcsZVC6Kjo9m/f3/pcGpqKi1btjzlMl988UVp44d169ZV6zPHzZkzh2+++YaPP/643IRU3WlFR0czYsQIfH19iY2NpVOnTiQnJwOUlo+Li2Pw4MH8+eefFS4TITyRr58fbfp3B2z89N+KGygJD2P2TbYz/fPExhklJSU6NjZW79q1q7RxxpYtW04o880335zQOKNv376l484//3ydmpp60nS3bNlyQuOM2NjYchtnLF68WHfp0kUfPXr0hPdTU1P1+eefr7U2Gme0bdtWZ2Zm6szMTN22bVudkZFR7rTGjRuntdY6LS1NR0dH6/T0dJ2ZmamLiopK32/fvv1JDVCqYvZ6EuK4/1w3Qb846jL9zRuvmh1KncGLG2fIGVct8PHxYdasWQwbNowuXbowatQounbtyuzZs5k9ezYAl1xyCXFxcbRv355bbrmF119/HQCn00lKSkppowl3Xbt2ZdSoUcTHxzN8+HBee+01rFYrAJMmTWLdunUA3H333eTm5jJ06FB69uzJ7bffDsChQ4fw8TGuDjdp0oQnnniCvn370rdvX6ZOnVo6z6lTp7Jo0SIAhg0bRkREBPHx8QwZMoQZM2YQERHBtm3b6NOnDz169GDIkCE88sgjJzQ+EcKbDLxlLOBLyooNlNhsZocjqqB0Ofc6vEmfPn308R32cdu2baNLly4mRXRmtmzZwrvvvsvMmTNrfNqzZs0iJibGY35z5c3rSdQ/b0y4hYKCQ4RHt+fml14xO5xap5Rar7XuY3Ycp0POuDxMt27daiVpgXEm5ilJSwhPc92L07GoRmQfOELmkcNmhyMqUWeJSyk1XCm1QymVopR6pJzxU5RSG11/W5RSDqWU/LBCCFEnGkdE0qR1C5w6l3kPP2F2OKISdZK4lFJW4DXgYiAeGKuUOuGGiNZ6hta6p9a6J/Ao8LPWOrMu4hNCCIDxM17CxxJJYWEGa7//zuxwRAXq6oyrH5Citd6ltbYB84ARlZQfC8ytk8iEEMJN54sGAHZ+f+/kJ84Iz1BXiasVsN9tONX13kmUUkHAcODziiamlLpVKbVOKbUuLS2tRgMVQjRswybcjr9PFDbHUT5/cbrZ4Yhy1FXiKu/xDhU1Z7wc+LWyy4Ra67e01n201n2ioqJqJEAhhDjuwvtvRakA9q/bJs3jPVBdJa5UoLXbcDRwsIKyY6gHlwnrS7cmkydPLn16R8eOHQkLC6tWnEJ4s869+xMcGoFDZzLn/slmhyPKqotfOWM8E3EXEAv4AX8BXcsp1xjIBIKrO21PfHJGferWxN1//vMfPWHChCrjrC6z15MQlcnLydEzR1+nXxo9Sh9ISTI7nBqHFz85o04esqu1tiul7gaWAlbgXa11olLqdtf42a6iVwHLtNb5NTbzxY/A4c01NjkAmneHi08+izquPnVr4m7u3Lk8+eSTFY4Xoj4JDg2lacc2HN6xiS+efJ67Pvif2SEJlzr7HZfW+jutdUetdTut9TOu92a7JS201u9rrcfUVUy1pT51a3Lc3r172b17N+eff36l8xOiPrn+qWfxtURRVJzOqi8+NTsc4VLvuzWp7MyotuhyHqPlrd2aHDdv3jxGjhxZ+mxEIRqK7leez4aFC/hz/lIGXjXa7HAE8sinWlGfujU5bt68eZVeRhSivhoy+kYC/CIpcR5l7lPyRA2PYPZNtjP988TGGfWpWxOttd6+fbtu06aNdjqdp7wsKmP2ehKiuvYnJeqXRl+rXx59gy7Kzzc7nBqBFzfOkDOuWlCfujUBo1HGmDFjqryUKUR9Fd0hntDwSBz6GO9Pvt/scBo86dbEw0i3JkJ4phKbjdfGTcJJISMee5R2CWeZHdIZkW5NRI2Rbk2E8Ey+fn606tkRrQtZ/MJrZofToEniEkKIarr2kf/D19KU4pI0vp8jv+syiyQuIYQ4BQPGXwlY2brkV7NDabAkcQkhxCnoN/wKAgIisDvT+PDRh8wOp0GSxCWEEKdo5NP/h1IhpO8+QO4x6e+2rkniEkKIU9SsdVsaN2uKU2fz8YOPmB1OgyOJq5aY2a3JZ599RteuXbFYLLj/VGDPnj0EBgaWPo3j+O+7ytq9ezf9+/enQ4cOjB49GlsF/RHt27ePiy66iC5duhAfH8+ePXuqVQch6oNxM17ER0WQn5fBll9/NjucBkUSVy1wOBzcddddLF68mK1btzJ37ly2bt16QpnFixeTnJxMcnIyb731FnfccUeV0926dSvz5s0jMTGRJUuWcOedd+JwOE4q161bNxYuXMh555130rh27dqxceNGNm7cWPpj6LIefvhhJk+eTHJyMuHh4bzzzjvllhs3bhxTpkxh27ZtrFmzhqZNm1ZZByHqC18/P2LPTQBsLH/9A7PDaVDq/UN2n1/zPNszt9foNDs36czD/R6ucLzZ3ZqcyY96tdb89NNPfPLJJwCMHz+eadOmnZRYt27dit1uZ+jQoQCEhISc9jyF8FZX3PMAs1Zvpdh+lG/eeJXL7rjP7JAaBDnjqgWe1K1JWbt376ZXr14MGjSIVatWnTQ+IyODsLCw0kdDVTSPpKQkwsLCuPrqq+nVqxdTpkwp9+xPiPruvDtuAHzZ+fMGSiq4rC5qVr0/46rszKi2lPcYLTO6NSmrRYsW7Nu3j4iICNavX8+VV15JYmIijRo1OuV52O12Vq1axZ9//klMTAyjR4/m/fffZ+LEidWOR4j6IGHgEH59by4F+Qf56JGHmDDzFbNDqvfkjKsWeEK3JuXx9/cnIiICgN69e9OuXTuSkpJOKBMZGUlWVhZ2u73SeURHR9OrVy/i4uLw8fHhyiuvrHYDEyHqm+tmPItFNSLr4BHSD+6v+gPijEjiqgV9+/YlOTmZ3bt3Y7PZmDdv3knPCLziiiv44IMP0Frz+++/07hx49L7WxdccAEHDhzgqquuKm1I0adPH6644grmzZtHcXExu3fvJjk5mX79+lU7rrS0tNLLebt27SI5Obn0Pty4ceNYs2YNSimGDBnCggULAKNfrxEjRpRbx2PHjpGWlgbATz/9dMI9PCEaksYRkTRp0xKnzmX+Y0+aHU69J4mrFpjdrckXX3xBdHQ0q1ev5tJLL2XYsGEArFy5koSEBHr06MHIkSOZPXt26Xw2bdpUmjiff/55Zs6cSfv27cnIyCi9/Ldu3TomTZoEgNVq5cUXX+SCCy6ge/fuaK255ZZbamuRCuHxxj//Ij6WSAoLM1i77Buzw6nXpFsTD1Ob3ZpUJCcnh4kTJ/LZZ5/V2TzBu9eTEOVZ+t5stiz5Dj9rJPd88q7Z4VRKujURNaY2uzWpSKNGjeo8aQlRHw2bcDv+PlHYHEf5fMazZodTb0niEkKIGjRsyh0oFcD+9duleXwtkcQlhBA1qEPPPgSHRuDQmbw/ebLZ4dRLkriEEKKG3TDzRSwqjNyMNA7uTDY7nHpHEpcQQtSw4NBQmnVug9YFfPHk82aHU+9I4hJCiFpw3bRn8LU0pag4nZUL55odTr1SZ4lLKTVcKbVDKZWilCq3Axul1GCl1EalVKJSyqv7CWjI3ZrcdNNNxMbGls5n48aN1aqbEPVNwtUXAJqNn31vdij1i9a61v8AK7ATiAP8gL+A+DJlwoCtQIxruGl1pt27d29d1tatW096ry7Z7XYdFxend+7cqYuLi3VCQoJOTEw8ocy3336rhw8frp1Op169erXu169fldNNTEzUCQkJuqioSO/atUvHxcVpu91+UrmtW7fq7du360GDBum1a9eWvr97927dtWvXKudz7bXX6rlz52qttb7tttv066+/Xm65QYMG6WXLlmmttc7NzdX5+flaa63Hjx+vP/vssyrnY/Z6EqIuzLphon5x1KX6k2mPmx3KCYB1ug72/7XxV1cP2e0HpGitdwEopeYBI1yJ6rjrgIVa630AWuujNTHjw88+S/G2mu3WxL9LZ5o/9liF46VbEyHEcSOm3s/8J6ZxeNseigsK8A8KMjskr1dXlwpbAe5Pnkx1veeuIxCulFqhlFqvlBpXR7HVOOnWBB5//HESEhKYPHkyxcXFpxSjEPVJdId4QppE4tRZvD/5frPDqRfq6oyrvL43yj5rygfoDVwABAKrlVK/a62Tyn5QKXUrcCtATExMpTOu7MyotugG3q3J9OnTad68OTabjVtvvZXnn3+eqVOnVjtOIeqbCa+8wmvjJpGfnc7OTRtol3CW2SF5tbo640oFWrsNRwMHyymzRGudr7VOB1YCPcqbmNb6La11H611n6ioqFoJ+Ew09G5NWrRogVIKf39/JkyYwJo1a6odoxD1ka+fH9FndULrIha/8JrZ4Xi9ukpca4EOSqlYpZQfMAZYVKbMV8BApZSPUioI6A9sq6P4alRD79bk0KFDgHH29uWXX9KtW7dTWXxC1EsjH3ocP2tTikvSWDbnTbPD8W511QoEuARIwmhd+LjrvduB293KTMFosLEF+Gd1puuJrQq1NloNdujQQcfFxemnn35aa631G2+8od944w2ttdZOp1PfeeedOi4uTnfr1q209Z/D4dAxMTG6oKCg3Ok+/fTTOi4uTnfs2FF/9913pe9PnDixdBoLFy7UrVq10n5+frpp06b6oosu0lprvWDBAh0fH68TEhJ0r1699KJFi0o/36NHD71v3z6ttdY7d+7Uffv21e3atdMjR47URUVFWmut165dqydOnFj6mWXLlunu3bvrbt266fHjx+vi4mKttdZDhgzR3bp10127dtXXX3+9zs3NLbcunrCehKhLaxZ/pV8cdaV+ZcxNZofi1a0KpVsTDyPdmghRv71+0y0UFh4iKrYz45570bQ4pFsTUWOkWxMh6rdRz05FqVAy9hwk51iG2eF4JUlcQghRhyJbtiaseVOcOoePHyz3IUKiCpK4hBCijt34wgx8VAQFeZls+XWF2eF4HUlcQghRx3z9/Igb2BOwsfz1D80Ox+tI4hJCCBNcftdk/HyaYrMf5evXXjY7HK8iiUsIIUwy5M4bAT92rdpISQW9MIiTSeKqJfW9W5Ply5eXTqdnz54EBATw5ZdfVqsOQghDt3MHExQSgV1n8OHDU8wOx3uY/UOyM/3zxB8gN5RuTY7LyMjQ4eHhpd2aVJfZ60kIT5CVnqZnjh6rXxo9Wqcd2Fdn88WLf4BcVw/ZNc2q+Umk78+r0WlGtg5h4KiOFY5vCN2auFuwYAEXX3wxQdJdgxCnrHFEJBFtW5G2exvzH3uKO99/2+yQPJ5cKqwFDaFbE3fz5s1j7NixpxSHEOJv456bgY8lksLCdNYs+8bscDxevT/jquzMqLboch6jVd+6NTnu0KFDbN68mWHDhlU7DiHEyboMP5vN333LH+8vpN9Fl5kdjkeTM65a0BC6NTlu/vz5XHXVVfj6+lY7DiHEyS4afxv+vlHYHEf57LmnzQ7Ho0niqgUNoVuT4+bOnSuXCYWoIRc/dBdKBXBgY5I0j6+EJK5a4OPjw6xZsxg2bBhdunRh1KhRdO3aldmzZzN79mwALrnkEuLi4mjfvj233HILr7/+OgBOp5OUlBSaNGly0nS7du3KqFGjiI+PZ/jw4bz22mtYrVYAJk2aVNr0/YsvviA6OprVq1dz6aWXll7GW7lyJQkJCfTo0YORI0cye/bs0vls2rSpNHE+//zzzJw5k/bt25ORkcHEiRMBWLduHZMmTSqNZ8+ePezfv59BgwbVxmIUosFpl3AWwY0icehM3ps82exwPJZ0a+JhpFsTIRq2/Nxc3rrlDjQ2Rv17GtEd4qv+0GmQbk1EjZFuTYRo2IJDQ2nepS1aF/DVU3W7L/AWkriEEMLDjP3X0/haoiiypbHis4/NDsfjSOISQggP1PPaiwDYtPAHkyPxPJK4hBDCA5139VgC/KIocabxybTHzQ7Ho0jiEkIID3XVtIdRKogj2/eSn5trdjgeQxKXEEJ4qJbtOhAaEYVTZ/HR/fL0+OMkcdUST+zWpKw5c+bQoUMHOnTowJw5cyosN3/+fOLj4+natSvXXXddteIUQtSMm15+GatqQn5uOskbK/4+NyhmP57+TP+kW5Pqd2viLiMjQ8fGxuqMjAydmZmpY2NjdWZm5knlkpKSdM+ePUvHHTlypDqLoFrMXk9CeIsFLzyjXxx1qf7v9TfX2DSRbk081/L33+Lo3l01Os2mbeIYctOtFY73hm5Nli5dytChQ0ufnDF06FCWLFly0uOb3n77be666y7Cw8ONujdtWuW0hRA165opj/Hf626muCSNpe/NZtiE8juBbSjkUmEt8ORuTU51WklJSSQlJXHuuecyYMAAlixZclrzE0KcmQE3XQ1Y2b7sD7NDMV29P+Oq7MyotmgP7dbkdKZlt9tJTk5mxYoVpKamMnDgQLZs2UJYWNhpzVcIcXr6XnQZaz/5isLCQ8x5+EHGP/+i2SGZRs64aoGndmtyqvM/Xm7EiBH4+voSGxtLp06dSE5OPq15CiHOzKhnp6JUKJl7D5KdkW52OKaps8SllBqulNqhlEpRSj1SzvjBSqlspdRG19/UuoqtpnlqtyYHDhzgggsuAGDYsGEsW7aMY8eOcezYMZYtW1ZuZ5BXXnkly5cvByA9PZ2kpKTSe3dCiLoV2bI14S2b4dQ5fDLlMbPDMU2dJC6llBV4DbgYiAfGKqXKe+TxKq11T9ffU3URW23w1G5NDh06hI+PcXW4SZMmPPHEE/Tt25e+ffsyderU0nlOnTqVRYsWAUaCi4iIID4+niFDhjBjxozSziiFEHXvhudewEdFUJCfzqZVy80OxxR10q2JUupsYJrWephr+FEArfV0tzKDgQe11qfUZ7V0a1J9s2bNIiYm5qSzP7N483oSwkzfvPEqO1f+Sa9rh3He1afXkas3d2tSV40zWgH73YZTgf7llDtbKfUXcBAjiSWWNzGl1K3ArQAxMTE1HKq5arNbk7vvvrtWpiuEqFuX3XEf3GF2FOapq3tc5TV9K3uqtwFoo7XuAfwX+LKiiWmt39Ja99Fa94mKiqq5KIUQQni8ukpcqUBrt+FojLOqUlrrHK11nuv1d4CvUirydGdYF5dAxemT9SOEOF11lbjWAh2UUrFKKT9gDLDIvYBSqrly/ZBIKdXPFVvG6cwsICCAjIwM2Tl6KK01GRkZBAQEmB2KEMIL1ck9Lq21XSl1N7AUsALvaq0TlVK3u8bPBkYCdyil7EAhMEafZuaJjo4mNTWVtLS0GqqBqGkBAQFER0ebHYYQwgvVSavC2lReq0IhhBCV8+ZWhfLkDCGEEF5FEpcQQgivIolLCCGEV/H6e1xKqTRg72l+PBKoD0+qrC/1AKmLp5K6eKYzqUsbrbVX/hDW6xPXmVBKrfPWm5Pu6ks9QOriqaQunqk+1eVUyKVCIYQQXkUSlxBCCK/S0BPXW2YHUEPqSz1A6uKppC6eqT7Vpdoa9D0uIYQQ3qehn3EJIYTwMpK4hBBCeJV6n7iUUsOVUjuUUilKqUfKGa+UUv9xjd+klDrLjDiroxp1GayUylZKbXT9TTUjzqoopd5VSh1VSm2pYLw3rZOq6uIV6wRAKdVaKbVcKbVNKZWolLqvnDJesW6qWRevWDdKqQCl1Bql1F+uujxZThmvWC81Rmtdb/8wnkS/E4gD/IC/gPgyZS4BFmN0djkA+MPsuM+gLoOBb8yOtRp1OQ84C9hSwXivWCfVrItXrBNXrC2As1yvQ4EkL/6+VKcuXrFuXMs6xPXaF/gDGOCN66Wm/ur7GVc/IEVrvUtrbQPmASPKlBkBfKANvwNhSqkWdR1oNVSnLl5Ba70SyKykiLesk+rUxWtorQ9prTe4XucC24BWZYp5xbqpZl28gmtZ57kGfV1/ZVvVecV6qSn1PXG1Ava7Dady8sZbnTKeoLpxnu26pLBYKdW1bkKrcd6yTqrL69aJUqot0Avj6N6d162bSuoCXrJulFJWpdRG4Cjwvdba69fLmaiTjiRNpMp5r+yRSnXKeILqxLkB4/ljeUqpS4AvgQ61HVgt8JZ1Uh1et06UUiHA58A/tdY5ZUeX8xGPXTdV1MVr1o3W2gH0VEqFAV8opbpprd3vq3rVejlT9f2MKxVo7TYcDRw8jTKeoMo4tdY5xy8paK2/A3yVUpF1F2KN8ZZ1UiVvWydKKV+MHf3HWuuF5RTxmnVTVV28bd0AaK2zgBXA8DKjvGa91IT6nrjWAh2UUrFKKT9gDLCoTJlFwDhXq5wBQLbW+lBdB1oNVdZFKdVcKaVcr/thrN+MOo/0zHnLOqmSN60TV5zvANu01jMrKOYV66Y6dfGWdaOUinKdaaGUCgQuBLaXKeYV66Wm1OtLhVpru1LqbmApRqu8d7XWiUqp213jZwPfYbTISQEKgAlmxVuZatZlJHCHUsoOFAJjtNYed7lAKTUXo0VXpFIqFfgXxg1nr1onUK26eMU6cTkXuBHY7LqfAvAYEANet26qUxdvWTctgDlKKStGcp2vtf7GG/djNUUe+SSEEMKr1PdLhUIIIeoZSVxCCCG8iiQuIYQQXkUSlxBCCK8iiUsIIYRXkcQlhBDCq0jiEkII4VX+HxsuVCrUGvb9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now, try that the OPPOSITE WEDGE does not change its target wedgePop\n",
    "# WITH CUBIC\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [-0.2,-0.15,-0.1,0]\n",
    "coef2 = [0.6,0.65, 0.7]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c1 in range(len(coef1)):\n",
    "    for c2 in range(len(coef2)):\n",
    "        coeff1 = 0.\n",
    "        coeff2 = coef1[c1]\n",
    "        coeff3 = coef2[c2]\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio + coeff3 * ratio**3))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-4.*southArea)/2.  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                #northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(southX, 2.*L)\n",
    "                northPoint =     Point(0,      2.*L)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2, 3 =\",round(180./pi*maxAngle,2),coeff1,coeff2,coeff3) \n",
    "        if(RMSE[c1][c2] < 0.042 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(coeff1)+\",\"+str(round(coeff2,3))+\",\"+str(round(coeff3,3)))\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for shorted oppW, maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "a105cc9d-21a9-4af6-8112-2350d3def49b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.056659 for maxAngle, coeff1, 2, 3 = 162.0 -0.3 0.0 0.6\n",
      "RMS error is 0.049307 for maxAngle, coeff1, 2, 3 = 162.0 -0.3 0.0 0.65\n",
      "RMS error is 0.042518 for maxAngle, coeff1, 2, 3 = 162.0 -0.3 0.0 0.7\n",
      "RMS error is 0.03679 for maxAngle, coeff1, 2, 3 = 162.0 -0.3 0.0 0.75\n",
      "RMS error is 0.048314 for maxAngle, coeff1, 2, 3 = 162.0 -0.25 0.0 0.6\n",
      "RMS error is 0.041936 for maxAngle, coeff1, 2, 3 = 162.0 -0.25 0.0 0.65\n",
      "RMS error is 0.036775 for maxAngle, coeff1, 2, 3 = 162.0 -0.25 0.0 0.7\n",
      "RMS error is 0.033675 for maxAngle, coeff1, 2, 3 = 162.0 -0.25 0.0 0.75\n",
      "RMS error is 0.041598 for maxAngle, coeff1, 2, 3 = 162.0 -0.2 0.0 0.6\n",
      "RMS error is 0.037048 for maxAngle, coeff1, 2, 3 = 162.0 -0.2 0.0 0.65\n",
      "RMS error is 0.03469 for maxAngle, coeff1, 2, 3 = 162.0 -0.2 0.0 0.7\n",
      "RMS error is 0.035334 for maxAngle, coeff1, 2, 3 = 162.0 -0.2 0.0 0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now, try that the OPPOSITE WEDGE does not change its target wedgePop\n",
    "# WITH CUBIC, drop quadratic term\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [-0.3,-0.25, -0.2]\n",
    "coef2 = [0.6,0.65, 0.7,0.75]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c1 in range(len(coef1)):\n",
    "    for c2 in range(len(coef2)):\n",
    "        coeff1 = coef1[c1]\n",
    "        coeff2 = 0.\n",
    "        coeff3 = coef2[c2]\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio + coeff3 * ratio**3))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-4.*southArea)/2.  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                #northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(southX, 2.*L)\n",
    "                northPoint =     Point(0,      2.*L)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2, 3 =\",round(180./pi*maxAngle,2),coeff1,coeff2,coeff3) \n",
    "        if(RMSE[c1][c2] < 0.035 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(coeff1)+\",\"+str(round(coeff2,3))+\",\"+str(round(coeff3,3)))\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for shorted oppW, maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "a49da9c0-ca5b-496a-9ad0-2d27369eec3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.050694 for maxAngle, coeff1, 2, 3 = 162.0 -0.1 0.4 0.0\n",
      "RMS error is 0.046461 for maxAngle, coeff1, 2, 3 = 162.0 -0.1 0.45 0.0\n",
      "RMS error is 0.044153 for maxAngle, coeff1, 2, 3 = 162.0 -0.1 0.5 0.0\n",
      "RMS error is 0.047075 for maxAngle, coeff1, 2, 3 = 162.0 -0.1 0.6 0.0\n",
      "RMS error is 0.046839 for maxAngle, coeff1, 2, 3 = 162.0 -0.05 0.4 0.0\n",
      "RMS error is 0.044915 for maxAngle, coeff1, 2, 3 = 162.0 -0.05 0.45 0.0\n",
      "RMS error is 0.045397 for maxAngle, coeff1, 2, 3 = 162.0 -0.05 0.5 0.0\n",
      "RMS error is 0.054002 for maxAngle, coeff1, 2, 3 = 162.0 -0.05 0.6 0.0\n",
      "RMS error is 0.045733 for maxAngle, coeff1, 2, 3 = 162.0 0 0.4 0.0\n",
      "RMS error is 0.046557 for maxAngle, coeff1, 2, 3 = 162.0 0 0.45 0.0\n",
      "RMS error is 0.049888 for maxAngle, coeff1, 2, 3 = 162.0 0 0.5 0.0\n",
      "RMS error is 0.063364 for maxAngle, coeff1, 2, 3 = 162.0 0 0.6 0.0\n",
      "RMS error is 0.052769 for maxAngle, coeff1, 2, 3 = 162.0 0.1 0.4 0.0\n",
      "RMS error is 0.05875 for maxAngle, coeff1, 2, 3 = 162.0 0.1 0.45 0.0\n",
      "RMS error is 0.066682 for maxAngle, coeff1, 2, 3 = 162.0 0.1 0.5 0.0\n",
      "RMS error is 0.087832 for maxAngle, coeff1, 2, 3 = 162.0 0.1 0.6 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now, try that the OPPOSITE WEDGE does not change its target wedgePop\n",
    "# with QUADRATIC\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [-0.1,-0.05,0,0.1]\n",
    "coef2 = [0.4,0.45,0.5,0.6]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c1 in range(len(coef1)):\n",
    "    for c2 in range(len(coef2)):\n",
    "        coeff1 = coef1[c1]\n",
    "        coeff2 = coef2[c2]\n",
    "        coeff3 = 0. #coef2[c2]-coeff1\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio + coeff3 * ratio**3))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-4.*southArea)/2.  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                #northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(southX, 2.*L)\n",
    "                northPoint =     Point(0,      2.*L)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2, 3 =\",round(180./pi*maxAngle,2),coeff1,coeff2,coeff3) \n",
    "        if(RMSE[c1][c2] < 0.045 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(coeff1)+\",\"+str(round(coeff2,3))+\",\"+str(round(coeff3,3)))\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for shorted oppW, maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "52c6ade3-df0c-4d21-9ed7-93d74d4ce015",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.035969 for maxAngle, levelWeight,yLevel 162.0 1.53 0.6\n",
      "RMS error is 0.033389 for maxAngle, levelWeight,yLevel 162.0 1.53 0.65\n",
      "RMS error is 0.03116 for maxAngle, levelWeight,yLevel 162.0 1.53 0.7\n",
      "RMS error is 0.029419 for maxAngle, levelWeight,yLevel 162.0 1.53 0.75\n",
      "RMS error is 0.035673 for maxAngle, levelWeight,yLevel 162.0 1.56 0.6\n",
      "RMS error is 0.033725 for maxAngle, levelWeight,yLevel 162.0 1.56 0.65\n",
      "RMS error is 0.032304 for maxAngle, levelWeight,yLevel 162.0 1.56 0.7\n",
      "RMS error is 0.03154 for maxAngle, levelWeight,yLevel 162.0 1.56 0.75\n",
      "RMS error is 0.036328 for maxAngle, levelWeight,yLevel 162.0 1.59 0.6\n",
      "RMS error is 0.035105 for maxAngle, levelWeight,yLevel 162.0 1.59 0.65\n",
      "RMS error is 0.034532 for maxAngle, levelWeight,yLevel 162.0 1.59 0.7\n",
      "RMS error is 0.034701 for maxAngle, levelWeight,yLevel 162.0 1.59 0.75\n",
      "RMS error is 0.037735 for maxAngle, levelWeight,yLevel 162.0 1.62 0.6\n",
      "RMS error is 0.037239 for maxAngle, levelWeight,yLevel 162.0 1.62 0.65\n",
      "RMS error is 0.037456 for maxAngle, levelWeight,yLevel 162.0 1.62 0.7\n",
      "RMS error is 0.038433 for maxAngle, levelWeight,yLevel 162.0 1.62 0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now, try that the OPPOSITE WEDGE does not change its target wedgePop\n",
    "# linear weighting to 0.5 or so\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "maxWeight = [1.53, 1.56, 1.59,1.62]\n",
    "levelY = [0.6, 0.65, 0.7,0.75]\n",
    "RMSE = [[0.]*len(levelY) for x in range(len(maxWeight))]\n",
    "for c1 in range(len(maxWeight)):\n",
    "    for c2 in range(len(levelY)):\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                weight = max(1.0,1.0 + (levelY[c2] - L)/(levelY[c2] - 0.)*(maxWeight[c1]-1.0) )\n",
    "                wideAngle = min(maxAngle,pi/2.*weight)\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-4.*southArea)/2.  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                #northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(southX, 2.*L)\n",
    "                northPoint =     Point(0,      2.*L)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, levelWeight,yLevel\",round(180./pi*maxAngle,2),maxWeight[c1],levelY[c2]) \n",
    "        if(RMSE[c1][c2] < 0.032 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(maxWeight[c1])+\",\"+str(round(levelY[c2],3) ) )\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for shorted oppW, maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cee65d6d-e883-4245-a89d-0c31fbfe589b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.015377 for maxAngle, levelWeight,yLevel 162.0 1.86 0.35\n",
      "RMS error is 0.012704 for maxAngle, levelWeight,yLevel 162.0 1.86 0.38\n",
      "RMS error is 0.013311 for maxAngle, levelWeight,yLevel 162.0 1.86 0.41\n",
      "RMS error is 0.013401 for maxAngle, levelWeight,yLevel 162.0 1.89 0.35\n",
      "RMS error is 0.012235 for maxAngle, levelWeight,yLevel 162.0 1.89 0.38\n",
      "RMS error is 0.014713 for maxAngle, levelWeight,yLevel 162.0 1.89 0.41\n",
      "RMS error is 0.012448 for maxAngle, levelWeight,yLevel 162.0 1.92 0.35\n",
      "RMS error is 0.013097 for maxAngle, levelWeight,yLevel 162.0 1.92 0.38\n",
      "RMS error is 0.017072 for maxAngle, levelWeight,yLevel 162.0 1.92 0.41\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now, try that the OPPOSITE WEDGE does not change its target wedgePop\n",
    "# linear weighting to 0.5 or so\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "maxWeight = [1.86, 1.89, 1.92]\n",
    "levelY = [0.35, 0.38, 0.41]\n",
    "RMSE = [[0.]*len(levelY) for x in range(len(maxWeight))]\n",
    "for c1 in range(len(maxWeight)):\n",
    "    for c2 in range(len(levelY)):\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea  #no longer used. use linear instead\n",
    "                weight = max(1.0,1.0 + (levelY[c2] - L)/(levelY[c2] - 0.)*(maxWeight[c1]-1.0) )\n",
    "                wideAngle = min(maxAngle,pi/2.*weight)\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-4.*southArea)/2.  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                #northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(southX, 2.*L)\n",
    "                northPoint =     Point(0,      2.*L)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, levelWeight,yLevel\",round(180./pi*maxAngle,2),maxWeight[c1],levelY[c2]) \n",
    "        if(RMSE[c1][c2] < 0.015 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(maxWeight[c1])+\",\"+str(round(levelY[c2],3) ) )\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for shorted oppW, maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "173af1c4-c319-49d7-a09f-ae30b86422e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.02184 for maxAngle, levelWeight,yLevel 162.0 1.8 0.35\n",
      "RMS error is 0.017901 for maxAngle, levelWeight,yLevel 162.0 1.8 0.38\n",
      "RMS error is 0.015552 for maxAngle, levelWeight,yLevel 162.0 1.8 0.41\n",
      "RMS error is 0.01825 for maxAngle, levelWeight,yLevel 162.0 1.83 0.35\n",
      "RMS error is 0.014658 for maxAngle, levelWeight,yLevel 162.0 1.83 0.38\n",
      "RMS error is 0.013465 for maxAngle, levelWeight,yLevel 162.0 1.83 0.41\n",
      "RMS error is 0.016273 for maxAngle, levelWeight,yLevel 162.0 1.85 0.35\n",
      "RMS error is 0.013209 for maxAngle, levelWeight,yLevel 162.0 1.85 0.38\n",
      "RMS error is 0.013155 for maxAngle, levelWeight,yLevel 162.0 1.85 0.41\n"
     ]
    },
    {
     "data": {
      "image/png": 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09ysAEUm3u9Ptac3Fupb/GdaZuh3A1LqCO3T7Ze0jWTPZALQxxhysf9lVYxGR3liNNNIY4zvGaRmgu336VKkGI9aPV68zxgytYfhCrJufanw6zVHM6wqs08p/PtZphRKxfsA7wxjTsc6Rm4k6r63Yh4e/x7rLSJOWg0RkPNZRTyzWXtYHx5q0lGoqjDH1Pk0bysS6uWMk1lFPKtYRyDuOBhViaj1VKNaF4oNYv+Op8/BNNbobsc65b8E6bXCTs+EopRqBYJ2iP4B1qnA9tV/TbnbqdapQKaWUChX6rEKllFJhJZwfwAlAq1atTKdOnZwOQymlwsqKFStyjDG1/Zg/ZIV94urUqRPLly93OgyllAorInI0TxwJKXqqUCmlVFjRxKWUUiqsaOJSSikVVsL+GpdSqumpqKggIyOD0tL6PAFL1SYqKoq0tDS83vq89CA8aOJSSoWcjIwMWrZsSadOnZCfPFheHQ1jDLm5uWRkZNC5c2enw2kweqpQKRVySktLSU5O1qR1jESE5OTkJnfkqolLKRWSNGk1jKa4HPVUYQgp374dV1wcxcuX40lJoWzjRrxt21KRmYm3Qzr+wkIiOqaDy42ndQruhIQm2SiVUqo2mrgcUFlYhD8/jwNvvgk+H/kffojLG0H5jvr/HlAi3IhAROs4ItokENGhPVH9+xPRpSeRJ4wEcYNLD6iV+rmuueYaZs+eTevWrVmzZs0Rw/Pz87niiivYuXMnPp+P22+/nauvvprS0lKGDx9OWVkZPp+Piy66iGnTph3x/bKyMq688kpWrFhBcnIyr7/+OtU9BWjs2LFkZWXh8/kYNmwY06dPx+12s3PnTq666iry8vKorKzkoYce4pxzzmmMRRFywv4hu4MHDzbh8OSMyrw88t56i7Jt28h/620wBkTAGGK6JiEuQ0xsBsYP0QmlVFa4iIz3U1EM3uQ4ynNKcSclU5ZVgETHUrq7CCNuSvaA3yf4StzWjMTgjfETkeCh5eCuRKS3I/bciRDbGlJ6OLsQlKqn9evX07t3b0djWLRoES1atODKK6+sNnE9+OCD5Ofn8/DDD5OdnU3Pnj3Zs2cPXq+XoqIiWrRoQUVFBUOHDuXJJ5/klFNO+cn3n3nmGVavXs2MGTOYNWsW77zzDq+//voR8zl48CBxcXEYY7jooou4+OKLueyyy7jhhhsYNGgQN910E+vWreOcc85h+/bt1ZaluuUpIiuMMYN//hJyjh5xNSJjDMVffUX209Mp37KFyrw8cLlIOK073phy4iK+xhPpxxV9AFwe6DkWohPZ124AkRGxLJJyYr0xrCnYRXxkAj/kbSM5OpntB7JoFZlATkkxbbzR+Pxuuu7MIr7IR+p364jMK6bkh30UvbcZ2Iz3hQVExFWSdEprItLaEXHW9RDXDtoOcHoRKRWyhg8fXmMiAOvaUUFBAcYYCgsLSUpKwuPxICK0aNECsG7rr6ioqPaU/nvvvce9994LwEUXXcQtt9yCMeaIcePi4gDw+XyUl5cfHi4iHDxovSIxPz+fdu3aHWuRw4YmrkbgLy8n73//I/vxJ/AXFuLt0IGY/t1I7pRBFNuR8oXg8sLgaylN7sq82BiKPV5mb50NpoTVq+ZWO13j9yAuH8bvRVwVGONCxP/jCLHAUDDGTfTIeOLzW3HGxgKOy/bTeWcuRe/kg+QR9/5kIuN8JI/uhyR3hKG/gxatISYpKMtHqaMx7YO1rMts2HfY9mkXx9Tz+x7TNG655RbGjRtHu3btKCgo4PXXX8dln56vrKzkhBNOYPPmzdx8882cfPLJR3x/9+7ddOjQAQCPx0N8fDy5ubm0atXqiHHHjBnDsmXLOPvss7nooosAuPfeexk9ejRPPfUURUVFfPrpp8dUnnCiiasBGWM48PLL7Hv075iKCmJPOYUWPVqQUPkersqvIaYjle1HsKTnCLa7hVfWv0ph3mIKKgoAiDRtwB9F2YERYDyYsg4YA13juxAVCb1T2uFy+eiclEhJZRFtWsaRU5pNy8hIdhXuBCrYWbCdkspCMiO2UtTyAK+3LeQ1KSOhUEjL9jByldB/u5f4HT72bthBRNxm2s9/G1e8Cxl+A67kbnhPuAJcbkeXZVNS6Te4XcK+g6UkxESwcncmHRMTWbRtA12TU1myYz0d4lNYtXcLrWIS2J6XQaw3hvyyg4BBBEp8pcRFtmB/SR4d49uzuzCL/ik9+WH/DkZ0Pp6VWZu4sPdprMjcxLheJ7F2bwZDO/Ukv6yExOhYpxdBkzRv3jwGDhzIggUL2LJlC6NGjWLYsGHExcXhdrtZuXIleXl5jB8/njVr1nDcccf95PvVXaap6WarefPmUVpayq9+9SsWLFjAqFGjeO2115g0aRJTpkxh6dKlTJw4kTVr1hxOnk2ZJq4GcnDuXPbc/wCVubm0GDGC+ONa0HL/y0h5KXQcSkbX4bzoLuL7/RtY/92jACS7e+Ct6ELxrl4YXzzRUe1pnxDLmYNa0z4xmsEdk2gdF0mE21XL3YOHrltVf6o6vyyf/aX7+XbvKjYf2MLHA1cw4+AP9P/Bz/GbDSf94MU3vxU+NyRteYG4pHLyPv0beTGdSbzwEWJTuxAdFdnwC6wJ2HewlOQWkXy6fhf926fwzFfzOTW9Dy989zbHpfRm3o6P6NCiM+sOfkmCO40D8h2eylR83h1Q2QI8eeCPQNylGONGpLLa+YgxYMDtt/6+zYaoClieCbFl8OUuiCuG9zd5SCz28fTyOOJKCyiM7YS3LIPEhNPJKdzAiE6/5Puc7/nDKdfz2fbv+PPwy9h2YB99WqcFd8EdpWM9MmosL774InfccQciQrdu3ejcuTMbNmzgpJNOOjxOQkICI0aMYO7cuUckrrS0NHbt2kVaWho+n4/8/HySkmo+6xEVFcW4ceN47733GDVqFM8//zxz51pnZ4YMGUJpaSk5OTm0bt26cQocQoKWuETkBeA8YJ8x5rhqhgvwJHAOUAxMMsZ8G6z4fq6yrdvIfvwxCj6dT1T/fqT+6kziCv+D5GRDt7P4qsspPLl/BVt2vYUxhnhvKi0LfkXu/lQyy1Np3TKK3w3twHHt4zmpcxIxEQ1bJfGR8cRHxtM5/sdfzRtjWJOzhlXZq3jnhy8pWraMEctL6bsqjoPA9q4QnbKOLrmnUCQxzEv/DWWpx3P2WWcSF9V0HhtTk6IyH26XsGLHAdKTovnPitX0aZ3KCys/pFdyV+bueJ+2MZ3YUb4Ab2V7KmO+xSxOxhWZzTt7rAS0IQuIgHXli5CISPJcW4jyJ1Hm3k7n4kSyI8o4dXcSmbEuTtsZyf4YL312F1Ic4abdvmIq3S5a5lfg8hs8ZQZPhcEv4C2FCi9ElkBZFEQVQ3EMxBRDQWwlLQsNOfEHaJVv2JmymbQcWJf+MT13G5b0fpxzdhgWfD6fvjsNv//4CbpnlPLYiQNptWMznS6cQtbGr7jhkr9QWllJ1+RUp6sipKWnpzN//nyGDRvG3r172bhxI126dCE7Oxuv10tCQgIlJSV8+umn/OlPfwLg6aefBn48zfjSSy8xZMgQ3nzzTc4444wjdlALCwspKCigbdu2+Hw+PvroI4YNG/aT+U+aNIn169dTWlpKSkpYvl7rqAXtrkIRGQ4UAi/XkLjOAX6DlbhOBp40xhx5YrgKp+4qNH4/hZ9/Ttbd92AqKkg4ewQpnTbh2j4f2h/P/B7D+Vv2UnYXZdIutgMJ0pdvVw2gojyRXm1acmrXVkwc0pHOrULjNM6qfStZvmou7rfm0n/JXqLLYUcbN3vbG07osY+OVDCnciRrI/rRbeSVdElNYEiXZFyu8PodWWlFJQeKy6n0G77PyMftgk82bicx1sXcLV+QEpPM2vzPiXUnUxq5An9FAp7YLZjKaMRd8pNpeWlJBQW0i+hNTnkWI2J6s7mymKv2VbI2qQXjlm1ib7tWdPlyPRVtEvCsysYT76Ysy487wlh3gooBU2UZirVOisv6Q8DldWEqDe4YD/5SH56EKHz5ZUSkxFKeXUhkaktKswqIbNOC0t0FRLSOpjSzBE+yl4rsCqSlQAH4IwyucsFgEKz5+rGeRJDbEpIL4NvuQoe9hu9PTiUuO5/2E3/DGede0/iVEyAU7iqcMGECCxcuJCcnh9TUVKZNm0ZFRQUAkydPJjMzk0mTJpGVlYUxhjvuuIMrrriC1atXc9VVV1FZWYnf7+eSSy7hnnvuAayEddpppzFhwgRKS0uZOHEi3333HUlJScyaNYsuXboAMHDgQFauXMnevXs577zzKCsro7KykjPOOIPHH38cj8fDunXruP766yksLEREeOSRRxg9enS1ZWlqdxUG9XZ4EekEzK4hcf0LWGiMec3u3giMMMZk1TZNJxKX8fvJuvMv5L/7Lt527ehw+3gi1zwGwJLeo3nEl8mWg9vokdCLFr7BfL68O5hIxvZtw7n92zK6byqRntC8hmSMIbc0lzUzn8T1vzkkZxWREwfr0wVzfCFd3eXEF6bxlb8fi1MuJSI2kdF9Uymr8DOmbxsqjaFTckzQfhjt9xv8xlBQ6qPETkr7CsooKPWxPaeIkooyNu7LpqSykB8ObMbj9pNXuQmXCyR6CxgP7ugMTGUE4i7/ybQTvO3Jr9jD0FYj2FKwi0mterK6tIyrt+1je1oK/WZ/TkV6GmbB90S2jiFvnY+Ilj7K8rw/TUj2Z0+si8pSP5Ht4jDlFUR17YDx+Yjs3g1EiEjvgkRH405qjSs+CYmIwJWUCsaPO6EVxleBq0UcpqIciY6BigrweqGyEvF4MBUV4PFgSoqRqGj8+/fhahFPxbY1eNp2oXTJHCL6nULh2/8m6qQR7H9pOp6Bg9j95rt4u7THLNnGwdYekjIrKfMaIius+HPjoPz2GznjktuCUqcQGomrMZx33nm8/fbbREREBHW+mriOZWa1J67ZwEPGmC/t7vnAn4wxR2QlEbkBuAEgPT39hB1H8cPdY1W+fTtZd99D8TffkHzD9aSkLkc2fciOlO482f0EPtuzjPS4dFJdw/j0q274/V4uPiGNS0/swAkdE8PuSReZC+aw+1/TiVq3jcIIPxvShCUjhI6eYi7OF/z+OP5TNoKDJpZP/MdTQhTtE6LZX1TO0O6tKCz1cULHRPYcLGVQegK5heX0bhvHrv3F9GzTkj35pXRMjmFHbjFpidHsziuhVYtIdu4vJik2gp37i4mNcJNxoIQIj4td+4sB2HOwmPLKSrIKsin2FVPpyqPM5CGeg4h3P+IuwRWRjbjKcXkPWNeQXD67VAIY2kR3oqA8j7PaDSWzMJdL41LZXFHGL3fsITM+nk4ff46rTSoFSzbhTYggb6MQ0aLyiMQkXsFUGKI6JFKRW0DLYcdTmZ1Ni7PHUbk3k9hR51tPPek9APF6ccXEIO7Q23ExFeUgLvLnvgp9T2Tp/Tfj7d6D+De+IKYEfrh6OOP/9K+gxNJUE5dTNHEdy8xqT1wfAv9XJXH90RizorZpBvOIq2LvXnZMuBx/UREpV40noWIWvgNbmXvKVTyav4oKfwX9E0ay/LtTyDno4px+bbh2aGeOTw+/hFVVyerVZM2YTvHSrykVH+vTDC+fKeTEC6eVlJDncnFimaHIBS0ru3Mwws/G/IF4okr5JnsgElPIwaI2uLz5+MuTcHnz8FfE44o4YP/Pxvha4orMxlTG4orMAn8UrogcjN+DJ2ovBsETmYvgh4gcRHwYqQDx/SRWj1h7s11adqKispxTE7pS4ithuLslxb5yTs3O5mC5n+Tv1yHeSIo27kM8bgp3u3F5DKX7IxC3wVTaicktmEpDVNc2lGfmknjhOZRv20zCxOup2L6FlhdcQuWBA0R07gxud9jXdVW7t67mh4mXIgZO/uRromPjGn2emrgaVlNLXKF0V2EG0CGgOw3IdCiWIxR+uZjdU6ZgKiro+MgfiF7+R8qj4ply/BgW7v2MtBYdSa/4NZ98Ab3atOTuc7pwfv92YXcNqCbR/fvT5Zl/UbpxIzkzZhD7xRcMfL4UX5Sbpb3j8Ho8zO5ejAvYmroTv0sgZrf15cT5GCDBQKVABEI5Bg8ufPhxIfipfQcqUjyA0NIdQZw7mniJoY0nlujKSrpKBBGVFXQrq8BVUEiXnP34ygwRe5dQ6fNSdmAlfp9QeiACDOzL9yBuw+5KF+ADiQUDkZ3aUr4nh6QJ4yjf8gMJk26iYttm4i++lIqsLCJ79KgxKXmq+e1NU9G+S3+WnT+MXjO/4P2pV3Dpo+87HZJq5kIpcb0P3CIis7Buzsiv6/pWsJRu/IHdt96Kt3172k86kcgvb+Sr5A78pXUy+w6sZ2L3W/ngyy4sKijnshPb8+dzetMiMpQWbcOJ6tmTtMcfp2zLFvbPfAlfdjYjFy4Et5uhi63buSuT4nCXlJPfO4moSjc7UopoVRHB5vhs2pRHsS7+AJ0LXWxpVUHnfD87EoUuB/3ktoAOB/0UxAjtC/xURhqS88Dt9RNdIESKwRS6cAMVRR6M33rUVaXPja/YRWWZG2MMWeWHkkuC9c/tAr8hsmtH/IWFJJ57FpV5B2g55hwqDxyg5ZjRVB44QGSXLtU8uWCkNYm4xj/KCGXjbn+GTz7uT/rCTezfu4uk1A51f0mpRhLM2+FfA0YArUQkA5gKeAGMMTOAj7DuKNyMdTv81cGKrTaFixez+7e3ItHRdLh5JJ6l9zK/x3D+7N9Du8gEBkTfzDPvx5AY4+O1G05hYIcEp0MOisiuXWl7/30A+EtK8JeWUjBvHuLxUPDZQlzR0cj8+bgTE+ixaj8A1q9bikjHOpXX025+vV0u8PvB7YbKSnAJ+K0jML/9V1E1AJcL8bgRjwd3UhKS7CG6SzcAovv1w/h8RA8aiCkvJ+b44/GXlOBt06bG8ngSE4Gm+QqIhuD2eGDCL0n4+5vMm3olE2Z85nRIqhnTh+zWojwjg22/+CXeNm3ocEV3vOue42+d+/Ey+XSO60Zq0W/4ZE0Jlw7uwN3n92myR1k/16G2VbFjB+7kZIqWLMXbri0lq1bjbduGktXf401rT/m27XjbpFK+KwNvu3b4crLxpqZSWViINzUVf2kpnuRkJCISd0I8rpgYXFFRuJOSwOXCbT8XTjW+988+jnaZlbR+4z+k9zy+0eaj17gall7jaibKd+1i56SrwRjSJo/ALLuXR3sP5eXSnfyi6yUs/WYoX+wv5bazuvPbM7o3mWtZDenQ0UuE/aqGuDHWb0yi+/UDoOWZZzoSl/r5Eq+/ieg7n2bpAzeR/srXTofTqELltSaHjBs3jq1btx6OZdGiRdx2222sXr2aWbNmHX6GYXPQ9B9q9TP4y8rI+PXN+AsLSb9tLJ5l9/LHzr15qXQnI9uNY86ik9mWU8K/rzyR287qoUlLNRvDfnEzG/pE0uu7g6z5ao7T4TSqSZMmHX6kUnWmT59Onz59WLVqFQsXLmTKlCmUl5cTGRnJggULWLVqFStXrmTu3Ll89dVXR3z/+eefJzExkc2bN/O73/3u8NM1qvP2228ffuL8Ienp6cycOZPLL7/85xcyTGniqsIYw57776ds0yba/WESns1P89dug5hPEdf0/i2Llp5OjNfLm5NPZWj3pnsnmVI16fq7aYiBDY/e6XQojWr48OG1PjuwIV5rctVVVwHWa03mz59f7YN3CwsLeeyxx7jrrrt+0r9Tp07079+/WTxUtyo9VVhF7r+eJf/Nt0i+/Hxif7ifO9t1YHZlLqPaXcbzH3YgwiPMvPokOoXIo5qUCraBwy7gjYEP0PfbQpbOfp4h513buDOccwfs+b5hp9mmH5z90DFNIlivNbn77ruZMmUKMTExxxRvU9L8UnUtStauJfvpp4kbcxYpMR/walIrZkf4mdD9Oj5ZPJi0xBjev+U0TVqq2Rv8l+mUeWHvjCecDsUxh15rkpmZycqVK7nlllsOv9jx0GtNMjIyWLZsWbXXyOrzWpOVK1eyefNmxo8f3ziFCFN6xGXzl5eTdcef8SQl0aZ/Jm/kF/JIdAInpgznrQW98LiE5660kpdSzV2XPicx66RWDPgyh49n3s/oSXc33syO8ciosQTjtSZLly5lxYoVdOrUCZ/Px759+xgxYgQLFy4MRhFDlh5x2XKmP0PZpk20vbAbm/d+zsOtkhjSdijrV11ApNvD/yafSockTVpKHXLGtJnkx4Dv1deo9Pnq/kITc+i1IsARrzXJy8sDOPxak169egHWa00Ovdrk0GtNgBpfa3LTTTeRmZnJ9u3b+fLLL+nRo0ezT1qgiQuwnsOX+9xzxI8ZSnHRO/y2Q2fiIpPI2TaenEIf/7ziBLq11t8KKRWodfuubD+9M50zDLOfvNXpcBrchAkTGDJkCBs3biQtLY3nn3+eGTNmMGPGDMC69rRkyRL69evHmWeeycMPP0yrVq3Iyspi5MiR9O/fnxNPPJFRo0Zx3nnnAbBhwwaSk5MBuPbaa8nNzaVbt2489thjPPTQj0eWAwcOrDO+b775hrS0NP73v/9x44030rdvaL5wszE0+x8g+8vK2Db+F/iLiuh47n6uSzZsjIqhW+UfWLo+micuG8S4Ae0aMGKlmo6ignxWjDqFCi8Mn78Sb0TDvC27qf4AWV9r0jCa/RFXztNPU751K20v7Mxrnv1854EzW9/E4nXR3HF2L01aStUitmU8e8cMol02vDNtotPhhLzZs2cHPWk1Rc06cZVv307uzJeIH30a+4rf56nkZAYkncobn6UwrHsrrhvaxekQlQp5F/7lRXa3hnaffM/BA/ucDkc1A806ce3926O4IiJIbvs1d7dpR6S3BRvXjKFjcixPX368PhFDqXrwRkRS/IvRJB+Ej6bqUZdqfM02cRUtXUrh/Pkkj+zIq1F5rPZARyayvyCKJy4dRHy01+kQlQob597yd7Z2cNH5y53s2bnJ6XBUE9csE5cxhn2PPY63bSoH4r9gelIiAxKHsWR1Gr8e0ZV+afFOh6hUWHF7PEReOZG4Ylg4LSTeSKSasGaZuESE9o8/RrtRkdzXJpnYiDg2rh1Fz9Q4bjmjm9PhKRWWzpp4Bxu7e+jxTS6bVi12OhzVhDXLxAUQUbyOz72rWRnhoZ25mP0FkTx68QAiPW6nQ1MqbLW9+Q9EVMB3D4X/77quueYaWrdufcQTLw7Jz8/n/PPPZ8CAAfTt25cXX3zx8LBOnTrRr18/Bg4cyODB1d9xXlZWxqWXXkq3bt04+eST2b59e7XjjR079vA8Jk+eTGWl9abxnTt3MnLkSAYNGkT//v356KOPjq3AYaR5Ji5jKFn4Vx5r1Yq06K58vbqLniJUqgGcPPZK1veLpveqIlbM/5/T4RyTn/tak0M+++wzVq5cSU2/M63va03eeOMNVq1axZo1a8jOzuZ//7OW6wMPPMAll1zCd999x6xZs/j1r399DKUNL80zcYnw0sDz2eOC/Rnn0DM1nt+c0d3pqJRqEo77wyNUumDHUw84Hcox+bmvNamv+r7WJC4uDgCfz0d5efnhx0KJyOGH+ubn59OuXfP5zWmzfMiuMYatpfvoEj2EVfva8/j1fYjwNM8crlRD633iWcw6IYF+X+ex8PUnGHHpbcc0vYeXPcyG/RsaJjhbr6Re/Omkml/cWB+1vdZERBg9ejQiwo033sgNN9xwxPfr+1oTgDFjxrBs2TLOPvvsw286vvfeexk9ejRPPfUURUVFfPrpp8dUnnDSLLfWIsKUgfexac04xvRN5dSu+kJIpRrSafc8R0kUFLz4nNOhNJraXmuyePFivv32W+bMmcP06dNZtGjREd+vz2tNAueVlZVFWVkZCxYsAOC1115j0qRJZGRk8NFHHzFx4kT8fn8DljB0NcsjLoC/zduIr9LNnec0veehKeW0Dl2PY/Gp7RiwIJMPn/kT5/764Z89rWM9Mmostb3W5NBpu9atWzN+/HiWLVvG8OHDf/L9+rzWJFBUVBTjxo3jvffeY9SoUTz//POHr8ENGTKE0tJScnJyaN26deMVOkQ0yyMuYwzdW7fg5pHd6JisL4VUqjGMvf9VDrQE7xsfNMnXntT0WpOioiIKCgoAKCoq4uOPPz58Z+LRvtaksLCQrKwswLrG9dFHHx1+RUrg/NevX09paSkpKSmNXOrQ0CyPuESEG0/v6nQYSjVpCcltyTijF/3e28C7D1/HL/8y0+mQjsqECRNYuHAhOTk5pKWlMW3aNCoqKgCYPHkyd999N5MmTaJfv34YYw6/1mTr1q2H31js8/m4/PLLGTt2LGC91uS0004DrNeaTJw4kW7dupGUlMSsWbMOz3vgwIGsXLmSoqIixo0bR1lZGZWVlZxxxhlMnjwZgL///e9cf/31PP7444gIM2fOrPFUY1PT7F9ropRqPCVFB/lq1MkIcPInXxMdG1ev7+lrTRqWvtZEKaXqKTo2jgPnnUrqfnj/Xn0Ar77WpGFo4lJKNaoL/vgvdrYVOnz2AweydzsdjmoCNHEppRqV2+Oh8tILSSyEeffoUZc6dpq4lFKN7pzJD7Kps5tuS7LYuWmV0+GoMKeJSykVFInX30R0GSy9/8inSCh1NIKWuERkrIhsFJHNInJHNcMTReQdEVktIstEpPpHMiulwtKwX9zMht4R9Pr2IGu+muN0OCqMBSVxiYgbmA6cDfQBJohInyqj3QmsNMb0B64EngxGbEqp4Oly272IgQ2P3ul0KHUKldeaHDJu3LifxLJo0SKOP/54PB4Pb7755tEXMIwF64jrJGCzMWarMaYcmAVcUGWcPsB8AGPMBqCTiKQGKT6lVBAMOn08Gwa0oPfaUpZ8+GLdX3BQqLzWBODtt9+mRYsWP+mXnp7OzJkzufzyy4+yZOEvWImrPbAroDvD7hdoFfALABE5CegIpFU3MRG5QUSWi8jy7OzsRghXKdVYTvjzk5R5Yd8/H3M6lFqFymtNCgsLeeyxx7jrrrt+0r9Tp07079//8BPpm5NgPfKpuueQVK2hh4AnRWQl8D3wHVDtA86MMc8Cz4L15IyGC1Mp1di69juVWSe1YsCXOXw88wFGT7qr1vH3PPggZesb9rUmkb170ebOYztdGazXmtx9991MmTKFmJiYY4q3KQlWqs4AOgR0pwGZgSMYYw4aY642xgzEusaVAmwLUnxKqSA6Y9pMDsaA79XXwvYBvMF4rcnKlSvZvHnz4WcfKkuwjri+AbqLSGdgN3AZ8JMTsyKSABTb18CuAxYZYw4GKT6lVBC1bt+VBcM7MmDuDmY/+TsumPJUjeMe65FRYwnGa02WLl3KihUr6NSpEz6fj3379jFixAgWLlwYrGKGpKAccRljfMAtwDxgPfCGMWatiEwWkcn2aL2BtSKyAevuw1uDEZtSyhnnTfsvOfHQ4t1PqSgvczqcoxaM15rcdNNNZGZmsn37dr788kt69OjR7JMWBPG1JsaYj4CPqvSbEfB5KdA9WPEopZzVIj6JPWMGctwbK3nn/qu45P5ZdX8piELhtSa1+eabbxg/fjwHDhzggw8+YOrUqaxdu7YRlkTo0deaKKUcU1FexudnDSSyDAZ9vJgW8dapMn2tScPS15oopVQD8UZEUjx+FK3y4YN7mv7vkfS1Jg1DE5dSylHn/uYxtnVw0eWLHezZucnpcFQY0MSllHKU2+MhYuKviCuGhdOuOdw/3C9jhIqmuBw1cSmlHHfWlXeysZuHHt/ksGnVYqKiosjNzW2SG91gMsaQm5tLVFSU06E0qKDdVaiUUrVpc/PtRPz+Ib576FbGv7yUjIwM9JFuxy4qKoq0tGqfnhe2NHEppULCKWdfxZsvPEHvVUWs+fJ9Bo38pdMhqRClpwqVUiGj9+0P43fBtn/c53QoKoRp4lJKhYy+J49m/QkJ9FxfzsL/1fwYKNW8aeJSSoWU0+55jpIoKHh+Rt0jq2ZJE5dSKqR06Hocm09tS7ftfj7855+dDkeFIE1cSqmQM2baKxxoCZ7X3wvb156oxqOJSykVchJT2rNrZE/S9xjeffjIlzCq5k0Tl1IqJI2b+jJ7kyD5w6WUFOmr+dSPNHEppUJSdGwcuecOIXU/vD/tSqfDUSFEE5dSKmRd+Kdn2dlW6LBgIweydzsdjgoRmriUUiHL7fHgu+QCEgth3tSJToejQoQmLqVUSDv3pv9jcycX3ZZksXPTKqfDUSFAE5dSKuS1vHYy0aWw9P4bnQ5FhQBNXEqpkDfi4t+wsXcEvb7NZ+3XHzsdjnKYJi6lVFjo/Nt7cPlh/aN/cjoU5TBNXEqpsDBo5C9ZPyCWXmtK+WrOS06HoxykiUspFTYG3fEk5V7YM/1Rp0NRDtLEpZQKG90HnMYPJ7ai52Yfn778oNPhKIdo4lJKhZURU1/gYAyUv/IffQBvM6WJSykVVtqkd2frsI503uXnw6d+73Q4ygGauJRSYef8+/5LTjzEvP0JFeVlToejgkwTl1Iq7LSIT2LPqP60z4Z3H5jkdDgqyDRxKaXC0oX3vExmCrSZt5LC/P1Oh6OCKGiJS0TGishGEdksIndUMzxeRD4QkVUislZErg5WbEqp8OONiKTwwrNolQ+zp17udDgqiIKSuETEDUwHzgb6ABNEpE+V0W4G1hljBgAjgL+LSEQw4lNKhafzbn2cbWkuOi/awb7dW5wORwVJsI64TgI2G2O2GmPKgVnABVXGMUBLERGgBbAf0HtdlVI1cns8eK6YQFwxLJg6yelwVJAEK3G1B3YFdGfY/QI9DfQGMoHvgVuNMf7qJiYiN4jIchFZnp2d3RjxKqXCxOhJd7Gxm4cey3LY8v0Sp8NRQRCsxCXV9DNVuscAK4F2wEDgaRGJq25ixphnjTGDjTGDU1JSGjJOpVQYan3T74msgBX/d6vToaggCFbiygA6BHSnYR1ZBboaeNtYNgPbgF5Bik8pFcZOPfdq1veNoteqQr77/B2nw1GNLFiJ6xugu4h0tm+4uAx4v8o4O4EzAUQkFegJbA1SfEqpMNf7Dw9jBLY+ca/ToahGFpTEZYzxAbcA84D1wBvGmLUiMllEJtuj3Q+cKiLfA/OBPxljcoIRn1Iq/PU9eTQbjo+j1/pyFr35tNPhqEYkxlS91BReBg8ebJYvX+50GEqpELBz0yr2XXQZWe3cnD9njdPhhDQRWWGMGex0HD+HPjlDKdVkpHcfwOYhbem2rZKPZtzpdDiqkWjiUko1KWPuf4UDLcD9+rv62pMmShOXUqpJSUxpz66RPUjPMrz3yI1Oh6MagSYupVSTM+7eV9ibBImzl1BSdNDpcFQD08SllGpyomPjyD33ZNrshw/uu8rpcFQD08SllGqSLvzTv9nZRkhbsIED2budDkc1IE1cSqkmye3x4LvkfBILYN7UK50ORzUgTVxKqSbr3F8/zOZOLrotyWTXFv1dV1OhiUsp1aS1vPp6Ykth8X3XOx2KaiCauJRSTdqIS29jfa8Ieq3IY/03nzodjmoAmriUUk1ex9/chdsPax75o9OhqAagiUsp1eSdcObFrB8QS+81JXw15yWnw1HHSBOXUqpZGHTHk5R7Yc8zjzodijpGmriUUs1C9wGn8cOJyfTc5OPTVx5yOhx1DDRxKaWajRFTX+RgDJS9/Io+gDeMaeJSSjUbbdK7s21oOl12+fnw6SlOh6N+Jk1cSqlm5Zxpr5AbBzFvf0xFeZnT4aifQROXUqpZiUtsTeaofrTfB+/+9Wqnw1E/gyYupVSzM37qK2SmQJu531GYv9/pcNRR0sSllGp2vBGRFFwwklb5MHvqr5wORx0lTVxKqWbp/Nv+wfb2QudF29m3e4vT4aijoIlLKdUsuT0e3BMnEFcMC6ZOcjocdRQ0cSmlmq3Rk+5mYzcPPZblsOX7JU6Ho+pJE5dSqllLnXwbkRWw4qFbnQ5F1ZMmLqVUszbkvGtZ3zeKXisLWfnFe06Ho+pBE5dSqtnrdfuDGIEtj091OhRVD5q4lFLN3nGnnM2GQXH0WlfGF29PdzocVQdNXEopBQy565+URMKB5/7pdCiqDpq4lFIKSO95PJuGpNJ9WyVznv2L0+GoWgQtcYnIWBHZKCKbReSOaob/QURW2n9rRKRSRJKCFZ9SSo2Z9gp5LcD12jv62pMQFpTEJSJuYDpwNtAHmCAifQLHMcb8zRgz0BgzEPgz8LkxRh8ippQKmqTUDuwc0Z30LMN7f5vsdDiqBsE64joJ2GyM2WqMKQdmARfUMv4E4LWgRKaUUgHGTXuVfYmQOHsxZSXFToejqhGsxNUe2BXQnWH3O4KIxABjgbdqmpiI3CAiy0VkeXZ2doMGqpRq3qJj48g55yTa5MK70/QBvKEoWIlLqulnahj3fGBxbacJjTHPGmMGG2MGp6SkNEiASil1yIV/fp5dbYS0+RvIy81yOhxVRbASVwbQIaA7DcisYdzL0NOESikHuT0eyi8+l6QCmHvPFU6Ho6oIVuL6BuguIp1FJAIrOb1fdSQRiQdOB/S5K0opR51389/Y0tFF18WZ7N62zulwVICgJC5jjA+4BZgHrAfeMMasFZHJIhJ468544GNjTFEw4lJKqdrEXn0tLUrhi2nXOh2KCiDG1HSpKTwMHjzYLF++3OkwlFJN1NsX9KfLlgoiX3yK3iee5XQ4DUZEVhhjBjsdx8+hT85QSqlapP/2Ttx+WPO3PzodirJp4lJKqVoMPvMy1vePoff3JXw992Wnw1Fo4lJKqToNuONxKjyQOf1Rp0NRaOJSSqk69Rw4nI0nJtFrUwXz//OI0+E0e5q4lFKqHk6f+jwF0VD60ktOh9LsaeJSSql6aNuxF1uHdqDLTj8fPHmb0+E0a5q4lFKqns6571Vy4yDqrXlUlJc5HU6zpYlLKaXqKS6xNZmjjiNtH7z34DVOh9NsaeJSSqmjcMFdL5HVClrP/ZbCfH1loBM0cSml1FGIjI7h4AWnk5IHs+/VB/A6QROXUkodpfN/9zTb2wudPt/Gvt1bnA6n2dHEpZRSR8nt8eD61WXEF8OCe692OpxmRxOXUkr9DGOuuYcfurrp8XU2W9ctczqcZkUTl1JK/UwpN95KZAV889ebnQ6lWdHEpZRSP9Op465nfZ9Ieq8sZOUX+v7bYNHEpZRSx6DHlL9igC2PT3U6lGZDE5dSSh2D/qeey4ZBcfRaV8YX7/zT6XCaBU1cSil1jIbc/U9KI+HAc9OdDqVZ0MSllFLHKL3n8Ww6JZXuWyuZ+9zdTofT5GniUkqpBjD6vlfIiwVee4tKn8/pcJo0TVxKKdUAklI7sHNEVzpmGt5/9NdOh9OkaeJSSqkGct69/2FfIiR88AVlJcVOh9NkaeJSSqkGEtsynuyzT6RNLrw7TR/A21g0cSmlVAMaf+cL7EoV0uavJy83y+lwmiRNXEop1YDcHg/lF59DUgHMmTrR6XCaJE1cSinVwM675VG2dHTR7cvd7N62zulwmhxNXEop1Qhir76WFqXwxX3XOR1Kk6OJSymlGsHIy37Php5een1zgA0rFjgdTpOiiUsppRpJ2s1/xu2H7x+53elQmpSgJS4RGSsiG0Vks4jcUcM4I0RkpYisFZHPgxWbUko1hhNHT2BDvxh6ry5h2cevOh1OkxGUxCUibmA6cDbQB5ggIn2qjJMAPAOMM8b0BS4ORmxKKdWY+t/xd3we2P30I06H0mQE64jrJGCzMWarMaYcmAVcUGWcy4G3jTE7AYwx+4IUm1JKNZqeg0awYXASvX6oYMF/H3U6nCYhWImrPbAroDvD7heoB5AoIgtFZIWIXFnTxETkBhFZLiLLs7OzGyFcpZRqOKff+zwF0VAy80WnQ2kSgpW4pJp+pkq3BzgBOBcYA9wtIj2qm5gx5lljzGBjzOCUlJSGjVQppRpY24692Dq0A112+vngH793OpywF6zElQF0COhOAzKrGWeuMabIGJMDLAIGBCk+pZRqVOfc9yq5cRD11lwqysucDiesBStxfQN0F5HOIhIBXAa8X2Wc94BhIuIRkRjgZGB9kOJTSqlGFZfYmsyz+pK21/Deg9c6HU5YC0riMsb4gFuAeVjJ6A1jzFoRmSwik+1x1gNzgdXAMuDfxpg1wYhPKaWC4YK7XyarFbSeu4KignynwwlbQfsdlzHmI2NMD2NMV2PMX+1+M4wxMwLG+Zsxpo8x5jhjzBPBik0ppYIhMjqG/HGnk5IHH0y93OlwwpY+OUMppYJo3O+fZkd7odPnW8nJ2uZ0OGFJE5dSSgWR2+NBLr+E+CL4ZOpVTocTljRxKaVUkI259l5+6OKmx1fZbF+/3Olwwo4mLqWUckDyjb8lqgK+fuDXTocSdjRxKaWUA4ZecAMb+kTSe2UBqxd/4HQ4YUUTl1JKOaT77+/HAJseu9vpUMKKJi6llHJI/9POZ8OglvRaV8aX7z3rdDhhQxOXUko56OS/PEOpF3L/9Q+nQwkbmriUUspBnXoP5odTWtNjayVzn9NThvWhiUsppRw2atpM8mOB196i0udzOpyQp4lLKaUc1qptZ7af3oWOmYb3/36z0+GEPE1cSikVAs6f9l/2JULC+4soKyl2OpyQpolLKaVCQGzLeLLHnECbXHjvvolOhxPSNHEppVSIuODO58lIFdrPX0debpbT4YQsTVxKKRUivBGRlP5yLEkHYe7UK50OJ2Rp4lJKqRBy/m8fY0u6iy6LM9i9bZ3T4YQkTVxKKRViYq6+hpYl8MV91zsdSkjSxKWUUiHmjAlT2NDTS6/l+9n43UKnwwk5mriUUioEpd38Z9yVsPqh3zsdSsjRxKWUUiHoxNET2NAvml7fl/DNx685HU5I0cSllFIhqv8dj1Hphozp/+d0KCFFE5dSSoWonoNGsGFwIr02VrDgv486HU7I0MSllFIhbNg9/6YgGopnvuh0KCFDE5dSSoWw9p37sOW09nTd6Wf2U1OcDickaOJSSqkQd/a0V9jfEiLfnKOvPUETl1JKhbyE5LbsPqsPaXsN7zx4jdPhOE4Tl1JKhYEL7nmFrFaQMucbigrynQ7HUZq4lFIqDERGx5B//nBaH4APpl7udDiO0sSllFJhYtyU6exoJ3T6fCs5WducDscxQUtcIjJWRDaKyGYRuaOa4SNEJF9EVtp/9wQrNqWUCgdujwe5/GLii+CTqZOcDscxQUlcIuIGpgNnA32ACSLSp5pRvzDGDLT/7gtGbEopFU7GXDeNTV3c9PhqH9vXL3c6HEcE64jrJGCzMWarMaYcmAVcEKR5K6VUk5J4/c3sTnOTl7Pb6VAc4QnSfNoDuwK6M4CTqxlviIisAjKB240xa6ubmIjcANwAkJ6e3sChKqVUaBs2/iYYf5PTYTgmWEdcUk0/U6X7W6CjMWYA8BTwbk0TM8Y8a4wZbIwZnJKS0nBRKqWUCnnBSlwZQIeA7jSso6rDjDEHjTGF9uePAK+ItApSfEoppcJEsBLXN0B3EeksIhHAZcD7gSOISBsREfvzSXZsuUGKTymlVJgIyjUuY4xPRG4B5gFu4AVjzFoRmWwPnwFcBNwkIj6gBLjMGFP1dKJSSqlmTsI9NwwePNgsX948bwlVSqmfS0RWGGMGOx3Hz6FPzlBKKRVWNHEppZQKK5q4lFJKhZWwv8YlItnAjp/59VZATgOG45SmUg7QsoQqLUtoOpaydDTGhOUPYcM+cR0LEVkerhcnAzWVcoCWJVRpWUJTUyrL0dBThUoppcKKJi6llFJhpbknrmedDqCBNJVygJYlVGlZQlNTKku9NetrXEoppcJPcz/iUkopFWY0cSmllAorTT5xichYEdkoIptF5I5qhouI/MMevlpEjncizvqoR1lGiEi+iKy0/+5xIs66iMgLIrJPRNbUMDyc6qSusoRFnQCISAcR+UxE1ovIWhG5tZpxwqJu6lmWsKgbEYkSkWUissouy7RqxgmLemkwxpgm+4f1JPotQBcgAlgF9KkyzjnAHKyXXZ4CfO103MdQlhHAbKdjrUdZhgPHA2tqGB4WdVLPsoRFndixtgWOtz+3BH4I4/WlPmUJi7qxl3UL+7MX+Bo4JRzrpaH+mvoR10nAZmPMVmNMOTALuKDKOBcALxvLV0CCiLQNdqD1UJ+yhAVjzCJgfy2jhEud1KcsYcMYk2WM+db+XACsB9pXGS0s6qaeZQkL9rIutDu99l/Vu+rCol4aSlNPXO2BXQHdGRzZeOszTiiob5xD7FMKc0Skb3BCa3DhUif1FXZ1IiKdgEFYe/eBwq5uaikLhEndiIhbRFYC+4BPjDFhXy/HIigvknSQVNOv6p5KfcYJBfWJ81us548Visg5wLtA98YOrBGES53UR9jViYi0AN4CbjPGHKw6uJqvhGzd1FGWsKkbY0wlMFBEEoB3ROQ4Y0zgddWwqpdj1dSPuDKADgHdaUDmzxgnFNQZpzHm4KFTCsaYjwCviLQKXogNJlzqpE7hVici4sXa0P/HGPN2NaOETd3UVZZwqxsAY0wesBAYW2VQ2NRLQ2jqiesboLuIdBaRCOAy4P0q47wPXGnflXMKkG+MyQp2oPVQZ1lEpI2IiP35JKz6zQ16pMcuXOqkTuFUJ3aczwPrjTGP1TBaWNRNfcoSLnUjIin2kRYiEg2cBWyoMlpY1EtDadKnCo0xPhG5BZiHdVfeC8aYtSIy2R4+A/gI646czUAxcLVT8damnmW5CLhJRHxACXCZMSbkTheIyGtYd3S1EpEMYCrWBeewqhOoV1nCok5spwETge/t6ykAdwLpEHZ1U5+yhEvdtAVeEhE3VnJ9wxgzOxy3Yw1FH/mklFIqrDT1U4VKKaWaGE1cSimlwoomLqWUUmFFE5dSSqmwoolLKaVUWNHEpZRSKqxo4lJKKRVW/h8Vv6FftmY7UgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now, try that the OPPOSITE WEDGE does not change its target wedgePop\n",
    "# linear weighting to 0.5 or so\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "maxWeight = [1.8, 1.83, 1.85]\n",
    "levelY = [0.35, 0.38, 0.41]\n",
    "RMSE = [[0.]*len(levelY) for x in range(len(maxWeight))]\n",
    "for c1 in range(len(maxWeight)):\n",
    "    for c2 in range(len(levelY)):\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea  #no longer used. use linear instead\n",
    "                weight = max(1.0,1.0 + (levelY[c2] - L)/(levelY[c2] - 0.)*(maxWeight[c1]-1.0) )\n",
    "                wideAngle = min(maxAngle,pi/2.*weight)\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-4.*southArea)/2.  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                #northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(southX, 2.*L)\n",
    "                northPoint =     Point(0,      2.*L)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, levelWeight,yLevel\",round(180./pi*maxAngle,2),maxWeight[c1],levelY[c2]) \n",
    "        if(RMSE[c1][c2] < 0.015 ):  #let's plot the \"keepers\"\n",
    "            plt.plot(yCenter,yUse,label=str(maxWeight[c1])+\",\"+str(round(levelY[c2],3) ) )\n",
    "plt.legend()\n",
    "plt.title(\"yUse vs. wideAngle parameters for shorted oppW, maxAngle =\"+str(round(maxAngle*180./pi,2)) )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "3529c07e-9299-41dd-9dd3-9caef0ed93b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(yCenter,yUse)\n",
    "idealX = [0,2,3]\n",
    "idealY = [1,1,0.5]\n",
    "plt.plot(idealX,idealY,linestyle=\"dotted\")\n",
    "plt.text(1.1,0.8,\"c1=\"+str(coeff1)+\",c2 = \"+str(coeff2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "6744e02b-b231-4860-b307-e14457d6a9e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(yCenter,yUse)\n",
    "idealX = [0,2,3]\n",
    "idealY = [1,1,0.5]\n",
    "plt.plot(idealX,idealY,linestyle=\"dotted\")\n",
    "plt.text(1.1,0.8,\"c1=\"+str(coeff1)+\",c2 = \"+str(coeff2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8204e029-718b-4766-bd9c-6839ae4a9735",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(yCenter,yUse)\n",
    "idealX = [0,2,3]\n",
    "idealY = [1,1,0.5]\n",
    "plt.plot(idealX,idealY,linestyle=\"dotted\")\n",
    "plt.text(1.1,0.8,\"c1=\"+str(coeff1)+\",c2 = \"+str(coeff2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "06e5d318-5756-418f-b61f-e06b7c288dac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.164057 for maxAngle, coeff1, 2 = 162.0 0.0 0.0\n",
      "RMS error is 0.073795 for maxAngle, coeff1, 2 = 162.0 0.3 0.3\n",
      "RMS error is 0.025686 for maxAngle, levelWeight,yLevel 144.0 1.9 0.36\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 8/15/22 - generate final comparison of HD1 and HD2 algorithms to simple constant-angle control\n",
    "# First, do the HD1 with coeff1 = 0.3, coeff2 = 0.3  (matching actuals for all HD1 states)\n",
    "# Then, do HD2 version with maxAngleRatio = 1.9, levelL = 0.36 ( \"  \"  \" all HD2 states)\n",
    "# plot the tractUse, compare to ideal dotted line\n",
    "pi = 3.1415926535\n",
    "maxAngle = 0.9*pi  #arbitrary max such that wedges don't stretch forever\n",
    "coef1 = [0.0]  #do trivial case first\n",
    "coef2 = [0.0]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c1 in range(len(coef1)):\n",
    "    for c2 in range(len(coef2)):\n",
    "        coeff1 = coef1[c1]\n",
    "        coeff2 = coef2[c2]-coeff1\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-2.*southArea)/3.  #this is the required area of each wedge except the south (shorted) wedge\n",
    "                northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(northDistance*tan(wHA), L+northDistance)\n",
    "                northPoint =     Point(0,                      L+northDistance)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2 =\",round(180./pi*maxAngle,2),coeff1,coeff2) \n",
    "        yUseHD0 = yUse # preserving output for all time\n",
    "\n",
    "# now repeat HD1, but with real HD1 parameters instead of trivial ones above\n",
    "coef1 = [0.3]\n",
    "coef2 = [0.6]\n",
    "RMSE = [[0.]*len(coef2) for x in range(len(coef1))]\n",
    "for c1 in range(len(coef1)):\n",
    "    for c2 in range(len(coef2)):\n",
    "        coeff1 = coef1[c1]\n",
    "        coeff2 = coef2[c2]-coeff1\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea\n",
    "                wideAngle = min(maxAngle,pi/2.*(1. + coeff1 * ratio + coeff2 * ratio*ratio))\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-2.*southArea)/3.  #this is the required area of each wedge except the south (shorted) wedge\n",
    "                northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(northDistance*tan(wHA), L+northDistance)\n",
    "                northPoint =     Point(0,                      L+northDistance)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, coeff1, 2 =\",round(180./pi*maxAngle,2),coeff1,coeff2) \n",
    "        yUseHD1 = yUse # preserving output for all time\n",
    "        \n",
    "# Now do HD2 simulation\n",
    "maxAngle = 0.8*pi  #arbitrary max such that wedges don't stretch forever\n",
    "maxWeight = [1.9]\n",
    "levelY = [0.36]\n",
    "RMSE = [[0.]*len(levelY) for x in range(len(maxWeight))]\n",
    "for c1 in range(len(maxWeight)):\n",
    "    for c2 in range(len(levelY)):\n",
    "        ySlices = 3*100    #divide the latitudes into 2*1000 slices\n",
    "        maxY = 3.\n",
    "        dy = maxY/ySlices\n",
    "        yUse = [0.]*ySlices  #akin to tractUse in HD code\n",
    "        yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "        yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "        for yy in range(ySlices):\n",
    "            yMin = dy*yy\n",
    "            yMax = dy*(yy+1.)\n",
    "            yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "            yCenter[yy]=yLayer[yy].centroid.y\n",
    "        MAP = Polygon([(0,0),(999,0),(999,999),(0,999)])\n",
    "        for yy in range(ySlices):\n",
    "            neededWedgeArea = 1. #default\n",
    "            L = (0.5+yy)*dy\n",
    "            centerPoint = Point(0,L)\n",
    "            if L > 1. : #wedges are perfect squares\n",
    "                southeastPoint = Point(1, L-1.)\n",
    "                southPoint = Point(0,L-1.)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                northeastPoint = Point(1,L+1.)\n",
    "                northPoint = Point(0,L+1.)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastPoly = Polygon([southeastPoint,northeastPoint,centerPoint])\n",
    "            else:  #south wedge will be shorted\n",
    "                bottomArea = L*L\n",
    "                ratio = 1. - bottomArea  #no longer used. use linear instead\n",
    "                weight = max(1.0,1.0 + (levelY[c2] - L)/(levelY[c2] - 0.)*(maxWeight[c1]-1.0) )\n",
    "                wideAngle = min(maxAngle,pi/2.*weight)\n",
    "                #print(\"L, wideAngle are\",L, round(180/pi*wideAngle,2) )\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * (pi - wideAngle)  #narrowHalfAngle\n",
    "                southX = L*tan(wHA)\n",
    "                southeastPoint = Point(southX,0)\n",
    "                southPoint = Point(0,0)\n",
    "                southTriangle = Polygon([centerPoint,southPoint,southeastPoint])\n",
    "                southArea = southTriangle.area\n",
    "                neededWedgeArea = (4.-4.*southArea)/2.  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                #northDistance = ( neededWedgeArea / tan(wHA) ) **0.5  #neededWedgeArea = tan(0.5 wideAngle)*(northDistance)^2\n",
    "                northeastPoint = Point(southX, 2.*L)\n",
    "                northPoint =     Point(0,      2.*L)\n",
    "                northTriangle = Polygon([centerPoint,northeastPoint,northPoint])\n",
    "                eastTriangle = Polygon([ centerPoint,southeastPoint,(southX,2.*L) ])\n",
    "                eastNeededArea = neededWedgeArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                a = 0.5 * tan(nHA)\n",
    "                b = 2.*L                  \n",
    "                c = -1.*eastNeededArea\n",
    "                eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                southeastPoint2 = Point(southX+eastdX,0)\n",
    "                northeastPoint2 = Point(southX+eastdX,2.*L+eastdX*tan(nHA) )\n",
    "                eastTrapezoid = Polygon([southeastPoint,southeastPoint2, northeastPoint2,centerPoint])\n",
    "                eastPoly = eastTrapezoid.union(eastTriangle)\n",
    "            #print(\"north tri area should have been\",neededWedgeArea,\" but is\",2.*northTriangle.area) #2 is to include west half      \n",
    "            #print(\"east wedge area should have been\",neededWedgeArea,\" but is\",eastPoly.area)\n",
    "            finalPoly = southTriangle.union(northTriangle.union(eastPoly))\n",
    "            #print(\"finalPoly area = \",finalPoly.area)  #debug, should equal 2\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE[c1][c2] = round(variance **0.5,6)\n",
    "        print(\"RMS error is\",RMSE[c1][c2],\"for maxAngle, levelWeight,yLevel\",round(180./pi*maxAngle,2),maxWeight[c1],levelY[c2])\n",
    "        yUseHD2 = yUse\n",
    "\n",
    "#OK, all three done.  plot results\n",
    "plt.plot(yCenter,yUseHD0,label=\"square HDs\")\n",
    "plt.plot(yCenter,yUseHD1,linestyle=\"dashed\",label=\"method 1\")\n",
    "plt.plot(yCenter,yUseHD2, linestyle=\"dotted\",label=\"method 2\")\n",
    "idealX = [0,2,3]\n",
    "idealY = [1,1,0.5]\n",
    "plt.plot(idealX,idealY,linestyle=\"dashdot\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "dc9a114c-73b3-4cf7-bfa7-d9af8d8d9ce2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LEqZ+YHYcITyaqcOnaq0XAyc8NVlrnaa1Xg2UuSKPqJk9GQWk5RYDuF0xX7Yzgzd+3+605aW9+irpkyc7bXniWMrfn6aTJ9HkzTfMjiKE1zK/DVW4rad+2sSl7/yJrY6v+z4Zq/Zk8r95O5wyVrrWmrK0NMozMpyQTJxIUPv2WMPC0FrLiYdC1AGPK+hKqZuVUmuUUmvS0827Jtrbrd+fzeLt6YztlWjqme0nMrZXIgFWC9OW7T3lZSmlaPLKKzR64olTDyaqpLVm/003k/LIo2ZHEcLreFxB11q/r7XurrXuHhvr/BOjhGHSgp3UC/ZnXG/37FwlNjyQYac3ZubaZHIKT/5IjS07m7JUY9CXIydvibqjlCKsf3/C+vXFFefvCOFL5BtM/MeWg7n8vjmV689uTlig+47fc/3ZzSkqs/HF6n0nvYzDH01j16BBlGdlOTGZqEr02KuIHDHC5eMBCOHtXPJtrZT6AugPxCilkoGnAH8ArfUUpVQjYA0QAdiVUvcAHbTWua7IJ461ak8mEUF+XHtWM7OjVKlD4wgu69qEqBD/k15G5BUj8G/aBL+oKCcmEzWRO/c3yg8dJPqaa8yOIoRXcMlla3VFLlurO7nFZUQEnXyhFKI6Bx58kNKkJJp9/jnKajU7jhAew9TL1oTnSHVcpuZJxby03M4fm1Nr9Rxbfj4Hn36a0uS67RdenFijJ5+i2YwZUsyFcBIp6OKo/ZmF9Hl5Pl+uOvlj0mb4es1+bvx0DX/tq/lx8OJ//iHnhx+xZdb1yG3iRKxhoSg/P+wlJRRv3Wp2HCE8nhR0cdS7i3ahUPRv28DsKLVyadcmhAf58dHSPTV+Tmjv3rRevIjgzp3rMJmoiYOPPMK+a6/Dln/qfQoI4cvc9xRm4VIHc4qYuSaZK7o3pVG9ILPj1EpooB+jzozno2V7SckuonFkcJXz2/LzsYaFYY2IcFFCUZXYe++l3iW7ZbhaIU6R7KELAN5fvBu71tx6Tkuzo5yUa85qhtaaT5bvrXI+e2kpu4deTPpbb7smmKhWQNOmhPXrB0Dpvn1yfboQJ0kKuqC4zMZP61K4tGsT4qNDzI5zUppGhXBhpzjW7cuuuiCUlxN5xQhCevZ0XThRIyU7drD74mFkfTbD7ChCeCS5bE0AkFlQSrnNToMIz2puryivuIywQD/psMRDaa05/N77RI68Ar/oaLPjCOG2TnTZmhxD93FlNjt+FkV0aIDZUU5ZuONSu7ziMkID/P4zQlzBn3+i/P0JOfNMM+KJaiiliLn1FsAo7uVp6fg39KwTNIUwkzS5+7hJ83dyyTt/UlxmMzuKU2w8kEPvF+ezcHvaf6ZlvPMuh55/QY7ReoDUF15k7+hR2PLyzI4ihMeQPXQflldcxrRle+jVoj5B/t7RuUfbRuEEB1j5YtV+zm3X8Jhp8VM/oPzQIWmS9wD1hg3DPy4Oi5z5LkSNyR66D5u+Ionc4nLGn9vK7ChO42+1MLxLYxZuSyOroBQwmm+11liCggho1szcgKJGgk/rRP3rr0MpRVlamrSqCFEDUtB9VGFpOVOX7OGcNrF0bhppdhynuqRrE8psml/+OQhA/oIF7L1iJGUHD5qcTNRWeWYme0dcQfrrr5sdRQi3JwXdR81cm0xmQSl3etHe+REdG0fQukEY3/99wPGIwhoRgV9srKm5RO1Zo6KIGjOaiIsvNjuKEG5PLlvzUcVlNhZuS2Nwpzizo9SJJTvSiQoJoFOTemZHEU6Uv2wZob16yYAuwqfJaGviGEH+Vq8t5gB9W8fSqUk98pcsRdu84wx+X1f0z0b233AjmZ98anYUIdySFHQfU2azc+V7y5m76ZDZUerc1nnL2H/TTWTM/NbsKMIJgk/rRNPJk4gee5XZUYRwS1LQfcwPfx9g5Z5M/K3ef+lWapNWTOhxDcub/6dlSnio8PPOQwUEYMvNpWDlKrPjCOFWpKD7EJtd8+7CXXSIi2CAhw2RejL6tmnAoc69+HBVilz25GXS3niD/bfeSrmMZy/EUVLQfcjsfw6yO6OA8ee28vrOVQ4+8wy5P/3ItWc3Y31yDn/tyzY7knCiBvfdR/zkSdLnuxAVSEH3EXa7ZtL8nbRqEMbgjo3MjlOn7CUllGzbTllKCpd3a0p4kB/Tlu0xO5ZwImtYGKFnnQVAwfLl0qWvEEjXrz5DKbh/UFv8reo/g5Z4G0tgIIkzPgObDeXnx419WlBSbkNr7fUtE76ocPVqCleuxJ6TgzUy0uw4QphGrkMXXqU8IwNLcDCW0FCzowgX0VqjS0qwBAXJjzbhE+Q6dB+2bGcGr/22jcLScrOj1Lm0iRPZdfHF6LKyYx7XWrNoezpFpXJNurdRSh0t5gcffoSMd981O5IQppCC7uW01rzx+3Zmrk3Gz+L9H3fU6NHE3jEe5e9/zON/78/mmo9WVegOVnidcuMHq7bbTQ4ihDnkGLqXW7knkzVJWTwzrCMBft5f0INPP53g00//z+Nd4yPp2DiCacv2MLpHvDTLeiHl70/cSy8evV+WmopfdPR/ftwJ4a28/xvex02av5OYsECuPDPe7Ch1quzgQdLeeBNbdvZxpyuluP7s5uxIy2fpzgzXhhMuo5RCKYUtL4+9V47i0AsvmB1JCJeRgu7F/tqXxdKdGdzcrzlB/t49mEXBn3+S+dFH2AsLTzjP0C5xxIQF8tFSuYTN21nDw6l//fVEjRpldhQhXEYKuhcLD/TjktMbc1XPRLOj1LnIyy+n1YL5+DdufMJ5Av2sXNUzgW2H8sgv8f4TBH1d9NXjCGrbFoDsH36gPENaZoR3k8vWhMezFxdjCQqq0byFpeX4Wy34W+W3rK8oT09n56DBRF1xBQ0fedjsOEKcMrlszcdMX76XPRkFZseoc+VZWezsP4Ds776v0fwhAX74Wy3Y7Rq73XN/zIqa84uNpdkXXxB77/+ZHUWIOiUF3QvtSM3jyZ828e3aZLOj1D2bjfDzzyf4tE41fso/yTn0enEea/dl1WEw4U6C2rbBEhiILTeXg089Tcnu3WZHEsLppKB7oXcW7iLIz8r1fZqbHaXO+cXEEDfhWQJbt67xc5rHhpJdWMav/3j/mPDiWCU7d5L3xx+UHTxodhQhnE4KupdJOlzAj+sOMLZXAtGhAWbHqVN5CxdSsqf2Z6yHBfrRt3UMczYelGZ3HxPSrRutfv+NsLPPBsCWk2NyIiGcRwq6l3l34S78rBZu6tvC7Ch1SttsHHr2WdJeevmknj+8axNScopZtCPdycmEu7OEhABQuGYNO88bSMHy5SYnEsI5pKc4L6K1JiTAj6t7JdIgomZnfXsqZbXS/Ouvq7zuvCqDOzaiQXgg05btZUDbBk5OJzxBYLv2hF9wQa0O1wjhzuSyNeFxnDWi1q//HCQqNIBeLeo7IZXwZNpmI3fOHCKGDJFugYXbk8vWvFx6Xgmr9mSaHcMlsr/6iv2334G94NQuy7vwtDgp5gKA3F9+IeW++ylcscLsKEKcNGly9xJTl+zmgyW7WfrQuTSODDY7zolpDdn7oF5TSF4DmbshpjVs+h78AiEgDLb+AnFdICcZ0rdAi/6wbyVYAyChJ3rBPEgNQy1/zZje+UoozgGljL9zkiG8EQRUPyb6gewipi7ZzT0D21AvWAbx8FURF1+MNSqa0N69zY4ixEmTgu4FsgpKmb4iiWFdGrtHMbfbQFlgx++Qe8AorKunQlAk5KXAoX+Mwl2a/+9zrAHG87QNGp0G6z6HoAho1BnWfwlNzoCyQlgzjejeZxF9YC0sewNCYmDb7H+XM/sBKC+GsEbQ+nw4vBO6Xw8xbcBWBvFnHhM1q6CUacv20rheMDf18+4TCcWJKaUI69sHgNJ9+zj07AQav/wSfvWlBUd4DinoXmDasj0Ultq4Y0ArcwIUZMDaaRAcBdt/g52/GwU1L+XfeaJbGvNZ/WHgM8aeeYMOkNgbUjdBq4Fg8YOSXIhqBuUlxn3Lv4PK6LIyitb9TciZPYw9cls5BNWDXfMgojHkp8KmH6BhJ/jnG2OvP6wBfHfTvznaXAjaDg07wjkP0SmynB7NovhgyW7G9kokOMC7B7ER1StN2kfZ/v2UZxyWgi48ipwU5+Fyi8s4+6X59GkVw7tjz6j7FeYdggNrjb/nPw8F6UbxLXFczxsYYTR75x2EVudBs37GXnqzPscU55OR4zjOmfDxNEJ79ar+CVobxXvT98a/WXth6RsQ1hCy9hitArZSMhMGc8/OLozq1oAhl10PFjm1xNfp8nKUnx9aa3RJSY3HChDCFU50UpzsoXu47Yfy8Lda6nbvPH0brHjXKIDrvzD2osHYk259vtGU3e9+4xh4UCQERx77/BjnZAs/7zziXniBkB49avYEpUBZ4bQR/z7W7wHj8R2/w/Y54BdE9MopfBowBzZCadFcAhp3No7rd77SmFf4HOVnfDVmffop2d99T8LH0/CLijI5lRBVkz10L1BSbiPQz8lNxRk7YPb9UJRlFHSUcXw7oRf0e9A4nt2sLwSEOHe9ZkjfTvK+XaxZtZTh6VNQdhugoe0Q4/h/51HQeqDZKYUJ8pcsJXfuHOKeeQZllcMxwj2caA9dCroH252eT2L9UKwWJ+xF2sqgMBN+vAP2LDaKd2CEcTJaaCwMfNo4Hm3CHqvWmoOPPka9YRfX/VnIxTlGS8SS12D5O8Yx/5Jc6HipcUx/wGMQ5f3jy580u804tFKSB3mpRuvMniUQGgMRTWDle9DpMuN8h80/Gj8OV08FexmccR389hi0GwrhcbByCpz3FOxdDId3Ge/9incg7nSI72G0Fp12hbHezN3QtDuUFRsnZPo5v9tjW34+uqxM9tSF6aSge5niMht9X1nAOW1iefWKLie/IFs5zHsalk82jjP7BUHXceAfBL1uN042M1lZaipJY8cRc+utRF5+WZ2ua83eTNbtz+bGvi2MY/ClBfDTeKMolRVBYDi0u8i47O7su0/5vACPUl4KqRuhcVfYPtc46bHNhfDz3cZjASGw4AXocRNs+9Uosu0ugi0/Gz+S6sVD5i4IrGe08NjLwD/E+BuOntMAGD+e7OXG9lhebDwWHGW0GCkLRCYY50Q06AilecalkGffDRu+gZD6MOg54xyPnrcYPwC2/gw9bzOWbys1fmDUgtaafeOuxl5YSLOZ36DkPAthIinoXmb6iiSe+GEjX9zUi94tT+JM3D2L4bubjT0lbTeOF0e3gA7DoUF75wc+Rbq8HPj32GZdefHXLUxdsoelDw0grl6lSwDTtsCXY6DgsHESYPth0KQbtL7AOGve05XkGZf5xZ1u7EkrZVzu98Pt0OYC4zBM0jJo3A1S/jKeYw0wfvjYy4z7MW0gY7txLkXi2bDtF+h4mbHs/Sth8EuOSxjrQe/x8MfT0HWs8QNy7cdw4SvGnnd+GvS9zzjs07yfsW3+8QwMeAS2zDLW3+f/YOHLxuWNDTrA7gVGK0BBBthKjMKPMn40lOZBy3ONz9BWCiOmGa+x/cVG68uexcZ064m3r8LVqynPzCJi0AV1+zkIUQ0p6F6kzGan/8SFNKoXxMxbe9e8q8qyIuM67b1LjT2a+q2g/VDjC7r90LoNfZLKMzKwRkW57Pjl/sxC+k1cwB39W3H/oLb/nUFro9AteR3mPWM8FhAOl7xjtGY07ua+Z8nbbcbern+IcZ1/RBzY7TD3EehwCWz5CdK3/luUjwhvDPmHjL3mblfD3zOg3RBoMQDWzYBBL0BuCuTshx63wJ5FEN0cIhONHwjRLY33zFZqnDh55D2srSPP09rYlgNCIHOPcWgoMBw2fAVtBhutCBu+Mk6A/OkuowWg1UBY/ArUSzDuF2YYy1QWiGlrdFDU/Xrjh0bqZhjxkfF/JCTa6KSoksK//yaweXOskZEn9VEIcSpMLehKqY+AoUCa1rrTcaYr4H/AEKAQuFZr/Vd1y/XVgv71mv08OHMD0647s2YDixxcD2s+gv2rIW2zUbyjmhtfeEERdR/4FCRdcy3Y7SRO/9Rl67xl+hqW7sjgt3vPoUlVHfUUZkJxNnw2wmhKBmNv8+K3zS/q6duNHxhZe4xj0e2HwaKXjcebdjf2Zo8IjTUuPwyqZxxu+fsz6H0HxLYz9lzPfQxyDgDa6PSnvMQozJ7gyPebUsYP2QYdjEK97E046y745T7jx0vLAcahAWNmo8UlbbPRtH/ZVKNV4ey7oGFHytMOsXPQECIuvJDGLzxv1isTPszsgt4PyAc+PUFBHwLciVHQewL/01r3rG65vlrQr5u2ivT8En4e36fqvfND/xjdq859zNgTiUqEcx6CDsNcF/YUaK3J+/13dGkZ9YZe5LL17s8s5II3FtOzRTTTrj2z+haQoixIWg77/oQ/3zaam+s1hdFfGAWhLhXnwIG/IKE3zJ9g/Mio1wQWTzQKdWkhlDn6vPcPgfieRjHv94CRM3MXnD/BKF6hscae9cnuQXui8hLjPImgSOMHT0xr4/OcfT+0PA/2Lvn3uH69BGh8OuxeRFHvt/Fr2AD/2BjjOUK4kOlN7kqpZsCsExT094CFWusvHPe3Af211gerWqazC3peaR4FR778qhAbHIvVYj06f6NQo0kupySHovKiap9fcf4SWwkNQoy97MziTEqPfHmcgEVZqB8US3peCQGBhdi1nZhg4wSfjKIMyu3lxhfy8knGteMADdrBJVMgrAF+Fr9j5rcoC9FB0QCkFqSiqXp7CLAGHDN/kF8Q9QLrobUmtTC12tce7Bd8zPyh/qGEB4RTbi8noyij2udXnj8iIIIQ/xBKbaVkFlc/OE3l+SMDIwnyC6K4vJjskuyj881cu5+SchtjeiQeU9Arz18/qD7+Vn8KywrJLcmBDV9C2lbjGvfgKONyt8SzjYILx85fmvufbalKB/4iNrQhVq3J+/V+CpqeQaNdiyFjOzmB4RSVFxp7zuUlRqc+pfnG1QsXPAdJf0LjbjRq3h+KssixWE5q26s4/3G3vSp41LaXe8A41LDjN9g6C9pdTOgvDxBuK6M8MIyMwBAi8g8TZAklI+IO6t10O4FB1Y8dIIQzuHtBnwW8pLVe6rg/D3hIa11ltXZ2QZ/09yTe2/BetfMtGLmAmOAYJv09ifc3vM+GazYA8NSfT/Hdju+qfK5CHTP/0gNLmXfFPABu++M2lh5YWuXzY4MbMH/kv/NnF2fzxdAvALjipxFszdpW5fM71e/07/w/X0Gj0Ea8fe7bAJzz1TnVFsX+8f2PmX9gwkCe6P0Edm2ny6fVn20/ss3IY+a//fTbua3LbRwqOMT5M88/Ol9iqqZtsmZ+F0W5378FtfL8T/d+msvbXM4/6f8wZvaYatdfef7J502mX9N+zN83n7sX3F3t8yvP//XQr2lfvz1fbf2K51Y+V+3zK89fcVuq0baXlEyMVkyKieX9UH82pOZD3/t4avvnfKfyq3zuqW57DUIaHDP/Mdvez1ewNXNrlc/3lG3vRG5vPpzbWl3OobwUzl/xME+rhpz35w4OLgxh+rUJPP/QHBl6VbiEu/cUd7z/Bcf9paGUuhm4GSAhwbnNmQMSBtA4rPrLtML8w447/7CWw+gSW/NLyIa1HEbPRv8eWRjbfiznJ574i2XjgRy+W5vGjtQ8WjcMZ2z7sZTYSoxLzw6s4dbcAnLSDxsjlcW2NTp+qfQFExkYefTvWzvfSrD/v8eIHzjzgWr30o60LhyZv0lYE8AoFs+c9Uy1r7l5vebHzN8+2jijPiIg4pjnx376G1HLVtL3hgewh/zb7Wbl+bs26ApAk/AmNVp/5fnbRLUBoF10u+M+f3tqHr9sOMhNfZsTFuT/n/njQuMAOLPRmf99vtbGSWhL3zBOGkMRt34mnPvE0fnDDu+B3GUMCGhA4+IAY6++OBdyk/9dTmiMceZ2kzMIG3AdZO5mQPeraJy+AVoMg4g4hrU8iy65SdW+/iNqu+0BBFn//RyObnsOt3a+lZzSnCqf7ynb3om0j24P9dtTnt2cZ858mA6xPZmQ9A3nXfouP8elcNrCSYwecGe1yxGirrjLHrpbNLm7M601F09aSkGJjT/uPeffzmRKC+HzkcaxPmUxLvvpcVPVC/MAWmvKDx7Ev7G518FvPJDDZe/+SY9m0XxyfY+T68QnPx02zjROyto6C5qeaVwC1qyPcb22thnzhccZZ6LbSmDwy5C2yThrvuOlxjXd0S1859i2GyooKeeF2Vv4aX0KC+7vT0xYIDtS81CHt3LL8mtpkmdl2vi/sNbxpZVCuPse+k/AeKXUlxgnxeVUV8x9zcLt6Ww8kMsrIzobRaWsCNZMg3++Ns5iH/KqcSZzeEOzo54yXVaG8vc3vZgDdGpSjwnDO/LQt//wvz+2c+8Fx7mUrTphsdDrNjjzRuM69oztxhjvO34zLv/qOg4OboDu1xmXX5WX/Pfqg/otnfJ6RO3Y7Jp9mYWkZBfx6Pf/sC+zkBvObk6wv3EZZeuG4dDwTEb90J6eMzbxq/8jDL1josmpha9ySUFXSn0B9AdilFLJwFOAP4DWegowG+MM950Yl61d54pcnkJrzdvzdtAkMphLuzYxTnT6+hrYMde4xveyD44dgMSDle7dy96rxtLktVdrNqKaC1x5ZgJr9mbx1vydnNO2AWcknmTXn1Z/uOqbf+9XPJu8zaB/H/eUS8J8QFZhKSPe/ZPDBaU0iQzmy5t60bPFfztyuuKWt5m++Tx2l8/HPXt0EL7AJQVdaz26mukauMMVWTzRhuQc/tqXzYThHfFfNQX+nm5cZnTR63DmDWbHcypt1wR3PZ3AViaN7X4CzwzvyKLt6czfmnryBb0yaT53S3a75rfNqZzfoSExYYF8eO2Z7M0o4Lz2DQgP8j/ucyLrxxExpg9/pC9n3T8zOP20q1ycWgjpKc5jrNqTSbddk/Fb+io06W4cJ+8yyuxYPuVwfgn1w2Tv2Vut2H2Y5bsOM/ufg+xIy+f1kV24rFvTGj+/sDCDcZP7MWCnP+PfW1+HSYWvO9ExdDfto1IcobWGvUvpseR6o5h3HQc3/uGVxTxv/gLKs7LMjnFCR4r53/uy+GLVPpPTCGcpt9mZMGszo95fwVvzdxDgZ+F/o07nktOb1Go5ISExjNgZS59lpfz+a/WXIArhbFLQ3dyLU7+g7NPLjLOiBzwOQ9/wyqZaW24uB+69l/S33jI7SrWmL0/ike/+4a15O/DkFi5ft25/NlkFpViUYnd6Ptee1YxNzwzil7v6Mvz0JlhO4oqGfo+9x4O3KGbt/aQOEgtRNXc5y11UVlbEod/e5JbkyRQFReN/8wJjPHIvZY2IoPnMb7CEhZkdpVovj+gMCl7/fTsHc4qZMLwjflb5bewpcgrLePKnjfy4LoVvbzuLMxKjeP/q7vg74TNsktCOm4L7cGnyV+zZuJLmnartwVoIp5GC7o7sdvj2RhptncVK1ZGO4z7w6mJ+hLudCHci/lYLr47oQly9ICYv2IW/VfHs8P90ryDcTLnNzso9mTzy3T+kZBdx17mtaNcoHMApxfyI8y95lgNX/UHumrtg1kqnLVeI6khBdzfFOTBvAmydxYSysYSecxc9m57Etc8eJP2dd7BlHKbh44+hzB6lrIYsFsUDg9qRX1xOZmEZdrs+qSZa4Tq3fvYXf2xJpWFEIF/d0tt5VytUEhnTiL8SW7DafoB6exfTrFm/OlmPEJVJQXcnGTvhowug8DBLIi/hi8yhLDu7udmp6pw9Lx9bXp7HFPOKnrq449FCrrWWvrzdiNaa+VvT6NE8mvAgf8b1TuSybk04p00soYF1+9XX+YVJfD9zGPa/poEUdOEiUtDdRWkBfD3O6GzkpgU0CWjDxIN5RIUGmJ2szjV86EGPPbnsSDHfmZbHXV+sY8Ilnepsz0/UzNIdGUxfsZf9mUVsPpjLzf1a8OiQ9pzTJtZlGWJi2vFa0+GU/PopBxL+pEn3s1y2buG7PG+XyBslLYf3+0PaFhjxITTpRovYMC7qHGd2sjplLyigZPceAI/fs80uLCO7sJQRU/7kmZ83kV9S9VCiom5MXrCTcR+tZP3+HEIDrUy4pBMPDDLnkFVGwpUkL4hiwxv3m7J+4XukoJstYwd8dpnRf/dV35Ac3Ytbp68l6XD147J7uqwvv2T30KGU7vP8a7q7N4tm7v/146qeCXz8514uemsJecVlZsfyelprpi7ZzU/rUwDwsyguOb0J8+8/h29uPYtxvRKdesJbbTTu3J0fLovimXNy2Lbnb1MyCN8iBd1MRdkw8zrwC4Lr50Dr83lv0W7mbU017UvIleoNH06jp58iwMnD4JolPMif5y45jenX92RfZiEz1yZX/yRx0opKbdz95Tqe+2ULR85HvLlfC14f2YWQAPc4mnj+6BcpDlC8N+9hs6MIH+AeW70vOrQRvhgNeSkw6nOIaExqbjFfrdnP5d2a0jgyuPpleDi/mBiiRo40O4bT9Wkdw3e3ncXp8ZForSmzaQL8vP8Hmqt88ude3l24C38/RXJWEQ8MastFpxmHp9zt0E33jv25+NtQui3Zx65eK2jZyT0GHBLeSb5lzFCSD1+NBXsZXDfn6EhbHyzeTbnNzm39vXuoTHtpKSmPPkbxtu1mR6kzXROiUEqxck8mfV6ez5RFuygpt5kdyyNprSksLT964uSwLo3p1KQeDcODmHp1d+4Y0MrtCnlFQ7rdTEQ+zPt9gtlRhJeTgu5qdjvMvh+y9sKIjyD+TAAyC0qZsXIfw09vQmL9UHMz1rGSHTvImzeP8vR0s6PUuZAAK20bhfPSr1sZ8r8l7EzLNzuSR1mx+zCD3lxMhyfnMnzyMspsdqJCA5h6TXdm3nYW57VvaHbEavUeegOzb6/PtMgkcnP2mx1HeDEp6K5UXgLfXAPrv4BzHoLEfy9lsVoUN/Rpzu1evncOENyxI63nzyP0bO+/lKdz00im39CTj687k+zCMm6evkbOgK8BrTWvzt3G6A9WUFhq4+7zWtO7RX3yij3zvbu558MUANM/GW92FOHFZPhUV/rjGVj6Ogx6AXrd7pWDrFTHlp2NNTLS7BimWL7rMOM+XMn/RnXlos5xZBWUEhni79bNxa6UXVjKqj2ZXNCxEXa7ptVjsxnWpTEvXtaZ4ACr2fFO2YyRp9FmezmJv8yiQRPv/+Eu6s6Jhk+Vk+JcJXkNLHvTGP609x3HTJq5NpnIYH8GdnD/5sNToW029o65ipAzziBuwrNmx3G53i3rs+D+/sRHhwDw8HcbKLdp3hx1OuFB/ianM8f21Dxmrk1mf2YhG5JzKLXZjzajz7ztLLrGR3rND56Y4WOYsukzEv54jKeu+dLsOMILSZO7KxzaCJ+PhIgmMOj5YyYVlJTz3C+bfWN8bbudqNGjCTvvXLOTmOZIMQfo3aI+C7enc+k7f7I3w/v7HTjCbjdaBedsPMSgNxfz0dI9bE/No35YAO+POwOrRWG1KLo5Tiz0FoOueoSWjcK4OHklxYVyLoVwPmlyr2uFmTC5B1j84dpZUP/Yprb3F+/ihdlb+e72s+iWIF2G+po/d2Zw++d/UVpup03DcD65rgf1Qrxzb/2f5Bye+HEjp8dH8vSwjhSUlDN5wU5u6NOc+mGBZsdzic3LfqHROzeyN2Eo3V78wOw4wkNJk7tZ5jwCRVlw88L/FPPiMhvvL95Dn1YxXl/MC1evxpabS9iAAR45CEtdOatVDD/ecTZTFu0iOauIsCDjv2RmQSnRXtCP/+QFO1m5J5PswlK2HMwlJiyQNg2NIUtDA/14cHA7kxO6VvuzhrD+0fqk5i6lrKQA/0DvvqJFuJYU9Lq08VvY8CX0ewAanfafyV+t3k9Gfgnjz+1qQjjXypzxOcUbNxJ2zjkgBf0YifVDefGyzkfv/7juAA9/+w8dG0cQ6G8hrl4wd5/X+pjmeneUW1zGd2uTySwoZXCnODo0jqBxZBCZBSXEhgVy5Znx3H9BWyJDPP+HyslSSpH/zHVM2PUhCWsm0/HsB82OJLyINLnXlb1LYfql0OQMGPcD+Af9Z5Yf1x1g/tY03rzydK86Vng8urycsgMHCEhMNDuK20vPK2Hi3K3syyykzKbZnJKLRcGyh88lMiSANXszKSqz0bN5fbfoge7btcmkZBfx+ap9HMwpRil4fWQXLu3a1Oxobknb7RRMHYA1KxO/u1biH+zeP9SE+zlRk7sU9LpQkg+Te4J/MNz4OwR7d3N6dbTdLs3sp+BAdhF/7szgiu7xAHSb8DuZBaVc0KEhb4/pSmpOCQn167YoaK35aX0Ks/85SJuG4fhbLdx1XmsAuj77G1mFZbRrFM4Ll53G6U0jjw4rK45vx7fvoJ95k7RLz6XPM1PMjiM8jBR0V/rtcfjzbbj+N0jo+Z/J5TY73/19gGFdGhPk7/nX11alcPVqDj7xJE0nvU1gq1Zmx/EKa5MyWbE7k4lzt+FnUQT5W9nw1AVYLIrVezPZn1nI6r2ZNIkM5vwOjWjbyDhmvT+zkKzCUjo3jaS4zMbP61M4XFDKzX1bkFNUxkfL9rD3cCG3ntOC/ZmFxIYHckZiNMt2ZvDEjxvZnV5AbHggGfklhAX48deT5+NvtZBVUEpwgNXrt2VnspWV8c1VXZjXWfHuw+vw8/POEyFF3ZCT4lxl13xYPhm6XXPcYg7w84YUHpy5geiQAK+/9hyl8G/SBP8mTcxO4jXOSIzmjMRoGkYEsfVgLp2a1MOmNUkZhVz94SqKymyEB/qRV1LOq79t58mhHbi+T3PWJ2cz/vO/6dcmlvX7s8kpKuOiznEoBR8s2c27i3YRGuDHz46hSAd1bMh746KJCgkgPiqEW/u15PIzmlJmsxNgtRzdC4/ygpP3XM3q70/mqKGsyPuVD2c9xS2XvGB2JOEFZA/dmbKS4L1+xvXmN/wGgWH/mcVu15z/xiL8rRZm39VXmiaF05Tb7BzILqKozEbrBuFkFpTy47oDDGzfkGYxoeQUljFl8S6+XLWPs1rFMK5XIj2aRWOxKDILSsnIL6F+aABfrt5P+7hw+raO9YlhfM1SWlrC6Cnd6LkZ7pu0Hquf7F+JmpEmd1f4/ErjZLhbl0J08+POMvufg9w+4y/eHt2Vi7s0dnFA18pbuJDQ3r2xBPrGNcZC1NbXj1xOx+83s++hoVx43USz4wgPcaKCLj+/nWX7b7B9jjHoygmKudaat+fvpEVMKEMc4zd7q5Lde0i+9TYyP/3U7ChCuK2LHv2Il26w8hl/oO12s+MIDycF3RkKM2HWPRDTBnreesLZDheU4m9V3D6gFVYvb2oPaN6MhI+nETVypNlRhHBboeH1uLjLQDZYylm44l2z4wgPJ03up0pr+GosbJ9rXKLWuOpOYrTWaI0cOxdCAFBaksdbt/Wg7QELF8/dZHYc4QGkyb2ubJ1l3M57sspivjs9n8yCUpRSXl/MU198kcPTPjY7hhAeISAwnMbhieyJ0nz/+2Sz4wgPJgX9VJSXGNecx7YzxjevwiPf/cOIKX/iyS0iNaHtdkqTD1Cemmp2FCE8xoXPTmfxuZqcjTKsqjh5UtBPxbL/QdZeGPQCWE98ycmqPZms3JPJ2J6JXt/Fq7JYiJ88iQYPPmB2FCE8RlS9WO4NvJzR+zexffY3ZscRHkoK+sk6tBEWvQIdL4NW51U566QFO6kfGsDoHgkuCmeO8qwsyrOyAKSrVyFqqdOQ8eyZF0vGZOlkRpwc+dY9GXY7/HQnBEfCkFernHVDcjaLt6dzY98WBAd4d9eYGe+8y65Bg7HlF5gdRQiPExHbiNWjWvPgRWXs2fW72XGEB5KuiU7Ghq8g5S+49D0IrV/lrMt2HiYyxJ+xvbx77xwgatSVBLZpjTVMxngW4mQMu20SLT/sT8Laz6Hl+WbHER5GCnptlRbAvGeMM9pPq/4a69v6t2TUmfGEB3n/4AuBLVsS2LKl2TGE8Fj1IpuREHExKe/NwhYzm2bnDjE7kvAg0uReW8vegryDMPglqOY4cUZ+CeD9g1eUZ2Vx6PkXKJMz24U4ZYF9byYjO5Dv5jxrdhThYaSg10bOAePM9o6XQkKvKmfdlZ5P7xfn8eO6Ay4KZ56iv/8m+6uvsOXkmB1FCI8X2+40Pr2lKZ92yOevrUvMjiM8iBT02pj3LGg7DHym2lnfXbgLq0VxdqsYFwQzV/i559J68SKC2rQxO4oQXuGG817AAsz8+VGzowgPIgW9ppLXwoYvofftEJVY5az7Mwv5/u8DjO6RQEyYd480Zi8wzmi3RkaaG0QIL9KpZQ/u+DOEUR9nsGW1nPEuakYKek1oDXMfhdBY6HNvtbNPWbQLq1Lc3K+FC8KZx15YyM5Bgzn84UdmRxHC63S76mFmDFDM2vE/s6MIDyEFvSY2fQ/7V8C5T0BQRJWzFpSU89O6FEZ0b0pcvWAXBTSHttmIvPQSgrtVPSCNEKL2up5zGX5nxfF1yV4OH95hdhzhAWS0teqUFcOkMyGoHtyyCCzVdw6TmluMAhpEBNVtNiGEV9u9Zz4Tpt5Jn/xobvifnCAnDDLa2slaOw1y9sEFE6ot5uU2OwANI4K8vpjnL1lK0T//mB1DCK/Wovm5DNtopfG6DPalbDc7jnBzUtCrUloAS16D5v2g5YBqZ3/t9+2Mfn8FZY7C7q201qS98Tqpz0uf00LUtci77+eRayx8N7f6q2uEb5Oe4qqy6n0oSIcBM6qdNaewjOnLk+jfNhZ/q3f/TlJKkfjpp9gyMsyO4rbKyspITk6muLjY7CiilqxWK5GRkcTExGBxg0GGBpx7Na+8Op0euQvIy0glPKah2ZGEm3JZQVdKDQb+B1iBqVrrlypNjwI+AloCxcD1WuuNrsr3H8W5RicyrQZCQs9qZ//4z73kl5Rzx4BWLghnHq01SimsYWFYw8LMjuO2kpOTCQ8Pp1mzZl4/ZK430VpTVlZGamoqycnJJCS4xxgMib3u4/D/3Ulm+h2c+e5Ms+MIN+WSn59KKSswGbgQ6ACMVkp1qDTbo8A6rXVn4GqM4m+elVOgKAsGVN+xQ35JOR8t28P5HRrSPq7qs+A9Xe4vs0kaO47yw4fNjuLWiouLqV+/vhRzD6OUIiAggCZNmlBQ4D6jBrbtM5jtrUL5JHozRYWZZscRbspV7Uk9gJ1a691a61LgS2B4pXk6APMAtNZbgWZKKXPaloqy4c9J0HYINDmj2tm/XLWPnKIyxnv53jmAsihUYCDWqCizo7g9Keaeyx2a2itr9Mh9NG9QQPnf082OItyUq7baJsD+CveTHY9VtB64DEAp1QNIBJq6JF1lyydDSQ70f6RGs4/ukcCkMV3pEh9Zt7ncQMSQISR8OBXlhl94Qnizrp3Hcat/O/I+mERxbrbZcYQbctW38vF2VSpfAP8SEKWUWgfcCfwNlP9nQUrdrJRao5Rak56e7vSgFGbCineh/TCI61yjp4QG+jG0c2PnZ3EjWmsKli9H2737DH5x6pRS7Ny50ynLatasGX/88YdTluUNdlsGkrPCj9kTbzU7inBDriroyUB8hftNgZSKM2itc7XW12mtT8c4hh4L7Km8IK31+1rr7lrr7rGxsc5P+udbUJpfo2PnJeU2xnywgkXb6+CHhZspXL6cfdddT96cOWZHEW6kf//+TJ061ZR1L1iwgAEDBlCvXj2aNWtmSgZX63Dj//HOaCvvJGygsNh9jvEL91Drgq6UildKVT126H+tBlorpZorpQKAUcBPlZYb6ZgGcCOwWGudW9t8pyQ/HVa+B50uhwbtq53927UH+HPXYaw+cKw0pEcPGr/2KuEDB5odRQgAQkNDuf7665k4caLZUVzG6udH124jSQ2w8v6PD5sdR7iZGhd0pVSCUmoZsBX4w/HYCKVUtT/PtdblwHhgLrAF+FprvUkpdatS6kjbUXtgk1JqK8bZ8HfX7qU4wbI3obwY+lf/H6XMZuedhTs5PT6Ss1vVr/tsJlN+ftS76CJUQED1Mwu31qxZMyZOnEjnzp0JDQ3lhhtuIDU1lQsvvJDw8HAGDhxIVlbW0flXrFjBWWedRWRkJF26dGHhwoUAPPbYYyxZsoTx48cTFhbG+PHjjz7njz/+oHXr1kRFRXHHHXdwpItpu93Oc889R2JiIg0aNODqq68mJyfn6POmT59OYmIi9evX5/nnn6/ydfTo0YNx48bRooV3D4JU2bVDHuPyv+y0fv8PSooKzY4j3InWukY34FeMS8ssQJbjsXpAUk2X4ezbGWecoZ1qzxKtl7xeo1lnrtmvEx+apf/YfMi5GdxQyuOP65xf55gdw6Ns3rzZ7AgnlJiYqHv27KkPHTqkk5OTdWxsrO7atav+66+/dHFxsR4wYIB++umntdZaJycn6+joaP3LL79om82mf/vtNx0dHa3T0tK01lqfc845+oMPPjhm+YC+6KKLdFZWlk5KStIxMTH6119/1Vpr/eGHH+qWLVvqXbt26by8PH3ppZfqsWPHaq213rRpkw4NDdWLFi3SxcXF+v/+7/+01WrVv//+e5Wv5/fff9eJiYlOfpfc+zOc+ew4Pf2i9vqXnx8xO4owAbBGH6cm1qZjmR7ARVpru1JKO34M5Cil6jnzB4apmvUxbtWw2TWTF+6kfVwE57Zr4IJg5rHl51O0cRMBzX1rL6guXPne8v88NrRzHON6N6Oo1Ma101b9Z/qIM5pyRfd4MgtKue2ztf+ZPrZXIhd3aUxKdhGNI2s+ut+dd95Jw4bGVaF9+/alQYMGdO1qjJp36aWXMm/ePAA+++wzhgwZwpAhQwA4//zz6d69O7Nnz+aaa6454fIffvhhIiMjiYyMZMCAAaxbt47BgwczY8YM7r333qN71S+++CKdOnVi2rRpzJw5k6FDh9KvXz8AJkyYwKRJk2r8mnzJJY98yKWfnoFf+i8Mtk/AUoNBo4T3q80x9FTgmAutHZ3D7HNqIg9xz8A2PDqknddfa2wNC6P5d98SPW6s2VGEEx0p5gDBwcH/uZ+fnw9AUlIS33zzzdHiHBkZydKlSzl48GCVy2/UqNHRv0NCQo4uLyUlhcTExKPTEhMTKS8vJzU1lZSUFOLj/z13NjQ0lPr1vf9w1smw+vlzY/OLOVRs4/tPHjQ7jnATtdlDfxWYpZR6EfBTSo3GaIJ/qeqneR+rRTGsi3dfpgZQnpGBJTwcS2Ag+PubHcfjfXVL7xNOCw6wVjk9OjSgyum12Tuvjfj4eMaNG8cHH3xw3Om1/UHbuHFjkpKSjt7ft28ffn5+NGzYkLi4OLZs2XJ0WmFhIYelR8ITOr/3o4Q8+R0266/Yr34Fi1X20n1djffQtdYfAQ8CV2B0EnMN8ITWuvqRS7zIou3pTF6wk+Iym9lR6tyhZ55lz+WXy7XnPmzs2LH8/PPPzJ07F5vNRnFxMQsXLiQ5ORkw9vR3795d4+WNHj2aN954gz179pCfn8+jjz7KlVdeiZ+fHyNGjGDWrFksXbqU0tJSnnzySexVbHt2u53i4mLKysrQWlNcXExpaekpv2ZPERwUyr4hnXnjYguf//662XGEG6jVZWta6x+01kO01h211oO11j/UUS63pLXm9d+28eXqffhZvLupHSDqqjHUv/FG6RXOh8XHx/Pjjz/ywgsvEBsbS3x8PBMnTjxaaO+++25mzpxJVFQUd911V7XLu/766xk3bhz9+vWjefPmBAUF8fbbbwPQsWNHJk+ezJgxY4iLiyMqKoqmTU/cWeTixYsJDg5myJAh7Nu3j+DgYC644ALnvHAPccXd73OJKqX9Xz+YHUW4AaV15Q7bTjCj0cS+Tmu9RSnVBvgAsAG3a6PvdZfr3r27XrNmjcvWt3h7Old/tIoXLzuN0T3cYxQm4Z62bNlC+/bV92Ug3JenfIYrP3qKhO+mkXXFQ3S45g6z4wgXUEqt1Vp3r/x4bXa9ngOODPPzGkZnMYuBd049nmeYNH8ncfWCuKxb5W7ovUtpUhIZU6Zgc5zIJIRwX6ddcifpB0NYs9KcHvuE+6hNQY/VWqcqpYKAPsBjwLPA6XURzN2s3H2YVXszuaVfCwL9vPvkk/xFi8h4dwq6qMjsKEKIaoREx7D28d78eHoh+XuXmh1HmKg2BT1dKdUKoxe31VrrEiCI4w+84nVCA/24qHMco3ygqT366qtp+dtv+NVFX/lCCKcbO/h1vs4qofCHV8yOIkxUm4I+AVgLfAgc6Tz5PIxhT71epyb1mDymG0H+3r13bi8pAcC/oXd3mCOEN/EPjmJDTj8Ov7ed1d9J07uvqs1lax8DcUBTrfXvjodXYgy04tVmrEziQLb3Nz+XpaWx85z+5M6Za3YUIUQtNb35Seb2UHyc9L7ZUYRJqi3oSqkWR25AI6CRY8Q1i9Y6TWt9qO5jmmdzSi6Pfb+RmWuSzY5S92w2Qvv1JaiD+5/ZK4Q4VmyzVqSc05IlUYUsXfeL2XGECWqyh74T2OH498gtCShWSs3wqr7cj2Pywp2EBfpx7VnNzI5S5/zj4mjyyisEJHj/eQJCeKNbz3+ZdimaDe89aXYUYYJqC7rW2qK1tjr+tWitLUAA0Mnx76t1HdIsO9Pymf3PQa7unUi9EO/u+jRv/gLKDhwwO4YQ4hS0iO/IiE2hdFtZyK6t882OI1zspLoA01qXa623A7dgnPXuld5ZuJNAPws39GludpQ6pUtLOfj446S+6rW/zYQLKaXYuXOnU5bVrFkz/vjjD6csy1f0fOIN7r3FwmfrXjY7inCxU+3TMxcIcUYQd6O1JsBq4ZrezagfFmh2nDqlAgJo/u1MGtx3n9lRhIfp378/U6eac1b1xIkT6dSpE+Hh4TRv3pyJEydW/yQfkNjubIZEJvBD8QG271xhdhzhQrUZbe14rgQ2OSOIu1FK8dLlnalp17iezj8uzuwIQtSK1ppPP/2Uzp07s2vXLi644ALi4+MZNcrrL7yp1ugzn6Ttbdezbu542nzhuu6xhblqcpb7dKXUp5VuXyillgNvAw/UfUzXSsst5p/kHKD2w0N6msMff8yB++7H7kOjVPm6Zs2aMXHiRDp37kxoaCg33HADqampXHjhhYSHhzNw4ECysrKOzr9ixQrOOussIiMj6dKlCwsXLgTgscceY8mSJYwfP56wsDDGjx9/9Dl//PEHrVu3JioqijvuuOPoD2O73c5zzz1HYmIiDRo04OqrryYnJ+fo86ZPn05iYiL169fn+eefr/J1PPjgg3Tr1g0/Pz/atm3L8OHDWbZsmRPfKc/VskVvihoGs7pBIduTNpgdR7hITc9y31XpthGjD/e2Wmuva9N5Z+EuLn1nGel5JWZHqXvl5ejSEiwBAWYnES707bff8vvvv7N9+3Z+/vlnLrzwQl544QUyMjKw2+289dZbABw4cICLLrqIxx9/nMzMTF599VUuv/xy0tPTef755+nbty+TJk0iPz+fSZMmHV3+rFmzWL16NevXr+frr79m7lyjb4OPP/6Yjz/+mAULFrB7927y8/OP/hDYvHkzt912G9OnTyclJYXDhw8fHaa1OlprlixZQseOHZ38TnmuNg+8RHa7MjbPfdPsKMJFqm1y11o/A6CU6qm1Xll5ulKqh9Z6VV2EM0N6XglfrNrHpV2bEBvu3cfOAerfeKPPHFYw1a8Pw6F/6nYdjU6DC1+q0ax33nknDRs2BKBv3740aNCArl27AnDppZcyb948AD777DOGDBnCkCFDADj//PPp3r07s2fP5pprrjnh8h9++GEiIyOJjIxkwIABrFu3jsGDBzNjxgzuvfdeWrRoAcCLL75Ip06dmDZtGjNnzmTo0KH069cPgAkTJhzzI6EqTz/9NHa7neuuu65G8/uCXqddgN/c00jc+htZA7cT1aKN2ZFEHavNSXG/n+DxOc4I4i6mLt1Nmc3Obf1bmh2lTunSUor+2Qh4/2EF8V9HijlAcHDwf+7nO0baS0pK4ptvvjlanCMjI1m6dCkHDx6scvmNGjU6+ndISMjR5aWkpJCYmHh0WmJiIuXl5aSmppKSkkJ8fPzRaaGhodSvX7/a1zJp0iQ+/fRTfvnlFwIDvf9HeG1Edb6WjKXhrHn1TrOjCBeodg9dKWXBGIBFKeObv+K3f0ugvI6yuVxWQSmfLU9iaOfGtIgNMztOncr56ScOPv4Ezb7+iuDOnc2O4/1quOfsbuLj4xk3bhwffPDBcafX9sdg48aNSUpKOnp/3759+Pn50bBhQ+Li4tiyZcvRaYWFhRw+fLjK5X300Ue89NJLLF68mKZNm9Yqiy9oecEwXh7zHHMa76d/wWH8Q6v/gSQ8V0320MuBUozL08qBsgq3zXjReOibD+ZitSjuGNDK7Ch1LnzwYOKem0DQaaeZHUW4sbFjx/Lzzz8zd+5cbDYbxcXFLFy48Oix7YYNG7J79+4aL2/06NG88cYb7Nmzh/z8fB599FGuvPJK/Pz8GDFiBLNmzWLp0qWUlpby5JNPYrfbT7isGTNm8Oijj/L7778fbcIX/zVmzARmHDoEaz42O4qoYzUp6M0x9sSTgRYVbs2BCK3103WWzsXObhXDykcH0rZRuNlR6pw1LIzIESOkuV1UKT4+nh9//JEXXniB2NhY4uPjmThx4tFCe/fddzNz5kyioqK46667ql3e9ddfz7hx4+jXrx/NmzcnKCiIt99+G4COHTsyefJkxowZQ1xcHFFRUVXudT/++OMcPnyYM888k7CwMMLCwrj11lud88K9SHyrQZTmdiHpsffIS6v6UInwbKqmJ0QppYIAm9a6rMJj/oDFMTa6y3Xv3l2vWSPXWNaGtts5+OhjRI4cSUi3rmbH8VpbtmyhfXsZ5MaTedNnuGH6ZLLef5u/Lz+Ne+75xuw44hQppdZqrbtXfrw2J8X9BpxR6bEzABlr04OUJSdTsHw55Yfkl7oQvqLzuDt4d2wQP4RvJic/0+w4oo7UpqB3xhj/vKJVQBfnxRF1LSAhgZa//0b4oEFmRxFCuNAlza8hF8WMqeOrn1l4pNoU9GygYaXHGgIFTksj6lT54cNorbEEBKCsVrPjCCFcaOR5d/HYd3Y6f/43xfk51T9BeJzaFPRvgc+VUp2UUiFKqdOAT4Gv6yaacCatNftvv53kO+TXuRC+yGK1Ejx8CJOGWpizoupudYVnqk1BfwzYgtHMngesALYBj9ZBLuFsWhN91VXUGzbM7CRCCJNceOMr2OP9mbrvV2zlMn6Dt6lxQddaF2ut7wBCgUZAmNZ6vNa6uM7SCadRFgv1hg0jYrAcOxfCVymLhaubXkq3FXZmvnSD2XGEk53MeOhhjltzpVQLpZT06ODmijZsIPu779FlZdXPLITwaoPOeZgBm+xkb15Lebl8J3iTGhd0pVQHpdTfQA7GCGw7gR2Om3BjOT/8SNqrr6LLvaaXXiHESfIPCGTL7ecz7XzFnLmTzY4jnKg2e+jvAAuAaCAXiALeA0485JJwCw2feJxmX3+FJTjY7ChCCDdw/YiXmJZso83yT7HbbGbHEU5Sm4LeBXhIa52N0cNcDvAAMKEuggnn0OXlKKUIkIErhAfr378/U6dOPeaxhQsXHtM1bP/+/QkKCiI8PJyIiAjOOOMMXnrpJUpKTOnI0q0FBYZQEHEZ9u8LWD35WbPjCCepTUEvBvwdf2copRIcz5fhe9xU8bbt7DxvIIV//212FCGO0lpXOejKqZg0aRJ5eXkcPHiQ1157jS+//JIhQ4ZQ0y6ufclpNzzC36dZmFH2I7qOPg/hWrUp6EuAkY6/ZwK/AouA+c4OJZxE2wlq147A5s3NTiLcyMsvv0yTJk0IDw+nbdu2zJs3D4CioiKuvfZaoqKi6NChAxMnTjxmD1gpxc6dO4/ev/baa3n88ccByMrKYujQocTGxhIVFcXQoUOPjsgGxt7zY489xtlnn01ISAi7d+9m69atnH/++URHR9O2bVu+/tp5XVqEhobSv39/fvrpJ5YvX84vv/wCwKpVq+jevTsRERE0bNiQe++912nr9DSBYeFE3TiUc3UaOmmp2XGEE9TmsrWRWuuPHXcfBV4EPgCuqoNcwgmC2rUj/r0pWCMjzY4i3MS2bduYNGkSq1evJi8vj7lz59KsWTMAnnnmGXbt2sWuXbuYO3cun3zySY2Xa7fbue6660hKSmLfvn0EBwczfvyxnRhNnz6d999/n7y8PGJjYzn//PMZM2YMaWlpfPHFF9x+++1s2rTJmS+XhIQEunfvzpIlSwBjdLi7776b3Nxcdu3axciRI6tZgncbfM4EBmaHsPOZB8yOIpygRgVdKWVVSi1USgUCaK3tWuvPtNbvaq2l61c3lDd/Aba8PLNjiAqSxl1N9nffA6DLykgadzU5P/0EgL2oiKRxV5M7ezYAtrw84/5vvwFQnpVF0riryZu/wLifnk7SuKvJdxSqsoM1G2zHarVSUlLC5s2bKSsro1mzZrRs2RKAr7/+mscee4zo6Gji4+NrNBzqEfXr1+fyyy8nJCSE8PBwHnvsMRYtWnTMPNdeey0dO3bEz8+POXPm0KxZM6677jr8/Pzo1q0bl19+OTNnzjzhOu666y4iIyOP3oYOHVqjbI0bNyYz0xiQxN/fn507d5KRkUFYWBi9evWq8Wv0Sv5BbMk6g7JVOcz57k2z04hTVKOCrrW2YYx/fjLXrQsXK8/IIPmuu8h4d4rZUYSbadWqFW+++SZPP/00DRo0YNSoUaSkpACQkpJCfHz80XkTExNrvNzCwkJuueUWEhMTiYiIoF+/fmRnZ2OrcAZ1xWUnJSWxcuXKYwr0jBkzOHTo0AnX8dZbb5GdnX30NmvWrBplO3DgANHR0QB8+OGHbN++nXbt2nHmmWfWeBneLPGxF3n4Fgsz0j8zO4o4RbUp0M8A7yqlEh177JYjt7oKJ06OX0wMzb76kuhr5YpCd5I4/VMiL7sUAOXvT+L0T492xWsJDiZx+qdEDBkCgDU83Lh/wQUA+EVFkTj9U8LPHWDcj40lcfqnhPXtC4B/XFyNc4wZM4alS5eSlJSEUoqHHnoIgLi4OPbv3390vn379h3zvJCQEAoLC4/er1h8X3vtNbZt28bKlSvJzc1l8eLFAMecjKaUOvp3fHw855xzzjEFOj8/n3fffbfGr6Mm9u/fz9q1a+nreJ9at27NF198QVpaGg899BAjRoygoMC3GxkbNG5Bl3odWBdUwm/LZpgdR5yC2hTjqcDVwG6gFCgDyh3/CjcT3LEj/g0amB1DuJlt27Yxf/58SkpKCAoKIjg4GKtj5L2RI0fy4osvkpWVRXJyMm+//fYxzz399NP5/PPPsdlszJkz55gm9by8PIKDg4mMjCQzM5NnnnmmyhxDhw5l+/btTJ8+nbKyMsrKyli9ejVbtmxxyussLCxk0aJFDB8+nB49ejDE8UPps88+Iz09HYvFQqTj3BKrjDzI7Re9xm2zyyl4+SWzo4hTUJuC/hBGs3uLSrcH6yCXOElpb75J2muvy2U64rhKSkp4+OGHiYmJoVGjRqSlpfHCCy8A8NRTT5GYmEjz5s254IILGDdu3DHP/d///sfPP/98tHn8kksuOTrtnnvuoaioiJiYGHr16sXgwYOrzBEeHs5vv/3Gl19+SePGjWnUqBEPPfTQKV8zPn78eMLDw2nYsCH33HMPl19+OXPmzMFiMb7q5syZQ8eOHQkLC+Puu+/myy+/JCgo6JTW6Q0axyYSGRXDlvo2du78zew44iSpmn7xK6VytdYRx3k8U2sd7fRkNdC9e3e9Zs0aM1bttg4+8SRa22n83HNmR/FpW7ZsoX379mbHOCULFy5k7Nixx1x+5ku84TOsjazMXQz6cTjnBcTy4lULzI4jqqCUWqu17l75cb8aPPHcI/MqpQYAqsLkFhhDqQo3ETfhWdk7F0LUWlR0S0aEtmL5rh2sXvANZw64wuxIopaqLejAh45/A4GPKjyugUPAnc4OJWrPlpuLPS8P/yZNjjn5SAghampYh/sZ9OxNbF33ohR0D1TtMXStdXOtdXNgxpG/HbcWWuuztNY/uSCnqEbmJ5+ya/CFlKWlmR1FeIn+/fv7bHO7r2rXqQ9zh0fz5rklbNyxwuw4opZq01Pc1aeyIqXUYKXUNqXUTqXUw8eZXk8p9bNSar1SapNS6rpTWZ+viRxxOQ2feFzObBdCnJLB17zKC1mZ5M99z+woopZccg25UsoKTAYuBDoAo5VSHSrNdgewWWvdBegPvKaUCnBFPm/gHxdHlI93Y+lu5FwGz+XLn13nNr0JL+xFo28Wk7pJBnbyJK7qFKYHsFNrvVtrXQp8CQyvNI8GwpVxADgMyMS4zl1UwV5UxMEnnqR0716zo4gKrFYrZWXSRYOnKioqwt/fv/oZvVTswNvJLPTjl1n/aUwVbsxVBb0JsL/C/WTHYxVNAtoDKcA/wN1a6/+M6aeUulkptUYptSY9Pb2u8nqM4s2byf3lF8odfVUL9xAZGUlqamqdDRMq6obWmsLCQg4cOEADHz58ldjvfL69uzH7wnZDwWGz44gaqvF16Ke0EqWuAAZprW903B8H9NBa31lhnhHA2cC9QEvgd6CL1jr3RMuV69ANtvx8rGFhZscQFdjtdpKTk32+W1FP5O/vT4MGDYiI+E+3Gz7FnroZ3jmLpIbjaH7729U/QbjMSV+H7iTJQHyF+00x9sQrug54SRu/MHYqpfYA7YBVronoeWy5uVgjIqSYuyGLxUJCQoLZMYQ4aZaGHfhnU3us3/1O8qCNNG3ZyexIohquanJfDbRWSjV3nOg2Cqh8uds+4DwApVRDoC1Gv/HiOHRZGXsuvYzUVyaaHUUI4aUKxlzLpEEW3lv0pNlRRA24pKBrrcuB8cBcYAvwtdZ6k1LqVqXUrY7ZJgBnKaX+AeYBD2mtM1yRzxNpu53IUVcS1udss6MIIbxUr8tuIa91CAvYRnrWQbPjiGq45Bh6XZFj6EIIUbd+XPgBv//8Jmda4rlm4hyz4whOfAxdxjL3QAUrVpC/bJlPXysrhHCN4f1v4sJ/IGRTEsVF2WbHEVWQgu6BDk/9kNQXXgQp6EIIF4h5/DaeHWnl+0WPmx1FVEEKugdq+s5k4idPQlnk4xNC1L0efW6nK4F8um8B+TlZZscRJyAVwYNordFaYwkIIKBZM7PjCCF8hLJYuDxsKI+/b+eX52WYDXclBd2DFCxdxp5LLqV0//7qZxZCCCcaeskTbGtpYV7oDopLCs2OI45DCronUQq/+vXxb9jQ7CRCCB9j9fODq66gZVQ+q+d+aHYccRxy2ZoQQogasdts7H3qdOx7bTSfth6rDw9gYya5bM3D5S9ejJbRu4QQJrJYreQEXkDZGs3CDx8yO46oRAq6ByjatIn9N99C1tdfmx1FCOHjOtw/gdevtfJNwAK5dNbNSEH3AEEdOtB0yrtEXnKJ2VGEED4uMDiER865mf/t303+xtlmxxEVSEH3AEopwvv3xxIaanYUIYSgRY/bSNvWiH13PoStvNzsOMJBCrqbO/TsBLK+kqZ2IYQbsfqzo8kZrIm2MXPOG2anEQ5S0N2YLiujZM9uyg5WHjpeCCHMdcZTk/joIgvfp3xudhThIAXdjSl/fxKnTSP2zjvNjiKEEMeoFxbNeQHdSC0u45cvXjQ7jkAKutsqP3wYW14eAMpqNTmNEEL8120XvsTzn9qwTZ9hdhSBFHS3lfbGG+waMgR7SYnZUYQQ4rhiYpqw4/JWvHYhbNr6ndlxfJ4UdDcVNXo0De65B0tgoNlRhBDihC4f/z5lYfDB6tfNjuLzpKC7qeCOHYm8/HKzYwghRJXCwuMYVdqKTt9lsuT7KWbH8WlS0N1MeXo6qRMnUp6ZaXYUIYSokWH9HqfDfs2KJVPNjuLTpKC7mYIVK8n6dDr2/HyzowghRI00a9+d729uxp/t89i1fa3ZcXyWFHQ3U+/iobRatJCAhASzowghRI3dc9HbzEg+TOZXL5gdxWdJQXcj9sJCAPyio01OIoQQtdOkSSu2HupJ2Oeb2LrsV7Pj+CQp6G7ClpvLzvMGkvXll2ZHEUKIk1L/pof5vq/i+51vmh3FJ/mZHUAYtM1GxEUXEdy5s9lRhBDipCR270urPR3psPtPyD0IEXFmR/IpSnvweLbdu3fXa9asMTuGEEKIIzL3kPdob3b79aTLpB/NTuOVlFJrtdbdKz8uTe5uIH/RIoq3bzc7hhBCnLro5mxNSaR4zTZ27d1gdhqfIgXdZFprUl94kbSXXjI7ihBCOEXpA/dz241W3pv/qNlRfIocQzeZUorEL7/AnptrdhQhhHCKs/teQdfNr7HYspt9+7aRkNDW7Eg+QfbQTXTk/AW/qCgCEhNNTiOEEM5zVYe7eOpjzZ/P3mh2FJ8hBd1EOd9+y76bbsYme+dCCC9zbt8xZMQH8Gf9wxTkHzI7jk+Qgm4mpUCBJTzc7CRCCOF0pz/6OAs6WPl64WNmR/EJUtBNFHn55SS8/z5KKbOjCCGE053W8QrOKg9i84LlZKUnmx3H60lBN4G22ylYtQpP7gNACCFqYrhtENf/opk18Razo3g9KegmyJ8/n31XX0PB4sVmRxFCiDo15ObnmHqlP5+23kNRcYHZcbyaFHQThPbrR9xLLxLap4/ZUYQQos4N6HM7H6UeYsMv75sdxatJQTeBJSCAyEsuQVmtZkcRQog6d9F5N1OQlEDUm+9RWih76XVFCroLaa1JefQx8hctMjuKEEK4jLJYyGs/hL2Bml9/fdzsOF5LCroL2bKyKFq3jrKDB82OIoQQLnXG3RP4ekwwtoyFYLebHccrSUF3Ib/oaFr8/BORI0aYHUUIIVzKYrUytceTDE/aw/Yv/2d2HK8kBd1FyjMy0GVlKKsV5Sdd6AshfI+93TB2LIojf9IH2MrLzY7jdaSgu0jKI4+y96qxcu25EMJnWfz8WDvsTJ4abuGTOS+YHcfrSEF3kagxo4keN1Z6hRNC+LRL736X4vowK2UmdpvN7DheRQq6i4QPGEC9iy82O4YQQpgqJCiUC6096LW0nFnvPmh2HK8iBb2OlezYweGPP8ZeVGR2FCGEcAs3XvISZ23V7N/wm9lRvIoU9DqW98cfZLz1NrqkxOwoQgjhFiKiGrD3sT5MORvWrv/E7DheQwp6HYu57TZazP4Fa2Sk2VGEEMJtXH7+y0TZNR8vecvsKF5DCnod0qWlAPg3amRyEiGEcC/BIdGM3ZvAze8U8sf0l8yO4xVcVtCVUoOVUtuUUjuVUg8fZ/oDSql1jttGpZRNKRXtqnzOVpp8gB3n9CdfRlQTQojjuviGN/jjDPg+7Ruzo3gFlxR0pZQVmAxcCHQARiulOlScR2s9UWt9utb6dOARYJHWOtMV+eqE3UZIz54EtmljdhIhhHBLcQltKTm3M+fpg+z6Z4XZcTyeq/bQewA7tda7tdalwJfA8CrmHw184ZJkdSQgIYGmb74hze1CCFGF24a/Tf/9kP/6Q2ZH8XiuKuhNgP0V7ic7HvsPpVQIMBj49gTTb1ZKrVFKrUlPT3d6UGfIm7+AcjfNJoQQ7qRedAN2Z3bGsjaVLet+NjuOR3NVQT9e92gn6gP1YmDZiZrbtdbva627a627x8bGOi2gs9gLC0l54AHS3nzT7ChCCOERGj75HHfeamXJ1vfMjuLRXDVKSDIQX+F+UyDlBPOOwoOb2y0hITT/7luUv7/ZUYQQwiPEt+7OjO3n03jNp2Tv30ZkfFuzI3kkV+2hrwZaK6WaK6UCMIr2T5VnUkrVA84BfnRRrjoRkJiIf+PGZscQQgiPUb/3fexbHMnue240O4rHcklB11qXA+OBucAW4Gut9Sal1K1KqVsrzHop8JvWusAVuZwt4733SXn8cbQMOCCEELUSFB3PpsaN+KHhYTbuWmV2HI/ksuvQtdaztdZttNYttdbPOx6borWeUmGej7XWo1yVydnsxUXowkKU1Wp2FCGE8DiNHnuZn3pYmLrgMbOjeCRXHUP3CQ3uvlvGOxdCiJPUrV1fei2KJPtACtvWL6Vtlz5mR/Io0vWrE9iLiijevh1AxjsXQohTcF3L23jgazt/vS1Dq9aWFHQnyP5mJnuGDadk506zowghhEfrOfAqfh0dwaSeOeRk7zU7jkeRgu4EERcPpdGEZwls1crsKEII4fGGXfU0uQEWpi94xOwoHkUKuhP4RUURdcUVZscQQgiv0KbVhYzYG0jTyes4mLTV7DgeQwr6KdBlZaQ88ihFmzaZHUUIIbxKn1YjCS2CL76WY+k1JQX9FJTu3Uv+woWUp6aZHUUIIbzKeVc9yCfjgjkctJXCglyz43gEKeinILB1a1rNn0fYgP5mRxFCCK/z8OnP81x6KhunTjA7ikeQgn6SyrOy0FpjCQ6WS9WEEKIOdOp1IVtWNSf0458pyJYRLKsjBf0kaLudfddcy8GHHzY7ihBCeLWs0SN45SIrv6yUvfTqSEE/GXY7UVddRfigQWYnEUIIr3bWuEcZ3KIe529dALYys+O4NSnoJ0H5+RF15UjCzz3X7ChCCOHVlMXCsDMexr7iMH+9IGe8V0UKei0V/vUXub/+KiOqCSGEiwR3uoh9SZHs/nsOpaUlZsdxW1LQayn7q69JffkVKehCCOEiFquVtXddxDPD/Zg66wmz47gtKei1FPfC8yR++gmWgACzowghhM+4dsQLxJdq5qXMpkz20o9LCnotaJsNZbUSkJBgdhQhhPApfn7+jCjuxSMf2Pj5tTvMjuOWpKDXUNH69ey6YBDFW6VfYSGEMMPo61/n7/aKBdZVaLvd7DhuRwp6LQS0aEFAfLzZMYQQwicFh0YQfcOFLGyo+XPtO2bHcTtS0GsouEsXEj54H0toqNlRhBDCZw3r9yytc+ysmPYeWmuz47gVKeg1kLdgAfbCQrNjCCGEz/MPDGXk7ngGLyjnp8+fMzuOW5GCXo3S5AMk334Hhz+aZnYUIYQQwKDHPuTJGxQ/5/1gdhS3IgW9GgFNm5A44zOirhpjdhQhhBBAVGwTRjYcyKTUXWxZ9YfZcdyGFPQaCOnWDb+oKLNjCCGEcBh6ybOk/R2N7XHpDvYIKehVSH1lIhlT3jM7hhBCiEpCwyPZ06Qjy2IK2bL5B7PjuAUp6Cegtab80EHK09LMjiKEEOI4ur7wDqv7Q9mGz8yO4hb8zA7grpRSNHn9dem8QAgh3FREvXjeaz6G0l/eYk/cXJqf49tDWsse+nGUZ2VRnp4OGEP3CSGEcE/Zbcay948Y9rz5mNlRTCfV6jgOT53KzkGDsWVnmx1FCCFEFeontmDO8IY8cUERqzfNMzuOqaSgH0fUyJE0fORhrJGRZkcRQghRjSE3vklxkOLjP581O4qppKAfR0BiIlFXXGF2DCGEEDXQtnlXLkqL5qwf0tjw5y9mxzGNFPQKbHl5HHzmGcoOHDA7ihBCiFoYcfb9JKbB0nkTzY5iGinoFRSt30DOd99TLsfOhRDCo3TuM4w/7mnCR00zyMjwzWGupaBXENbnbFovXkRwx45mRxFCCFFL1/d9mjI0H39xj9lRTCEFvRJrvXpmRxBCCHESEhL6cM/CAM57P4m9W9aYHcflpKALIYTwGm0uv51PzrPwwZJnzI7iclLQhRBCeI2zh91EdOtohh5eT272YbPjuJQUdCGEEF5lTJ8X6bijhB0T7jI7iktJQRdCCOFVWnXpw659cRT+tZaCgnSz47iMFHQhhBBex/b07fzfWCv/rHjd7CguIwVdCCGE1+ne52Z+90vkjDXfUpSbbXYcl5CCLoQQwivlJ1xH0leadU/faXYUl5CCLoQQwis16XcZ/7QI5NOwtRQWF5gdp85JQRdCCOGVLFYredePYWlLK1N+fNDsOHVOCroQQgivNXbQQ7Qt0OQtXUBJoXfvpUtBF0II4bUsViujs3sw8nfNr+9697F0P7MDCCGEEHVp2P3v8n/6DA5ErWGYrRyL1TtLn8v20JVSg5VS25RSO5VSD59gnv5KqXVKqU1KqUWuyiaEEMJ7+QcEcmGfy9lp1cxZ+rLZceqMSwq6UsoKTAYuBDoAo5VSHSrNEwm8AwzTWncErnBFNiGEEN5v0NmPMnK1jfLnZ2ArLzc7Tp1w1R56D2Cn1nq31roU+BIYXmmeMcB3Wut9AFrrNBdlE0II4eX8/AJpE9aWzGD44qfnzI5TJ1xV0JsA+yvcT3Y8VlEbIEoptVAptVYpdbWLsgkhhPABQ5+czg8XKfKTfkbb7WbHcTpXFXR1nMd0pft+wBnARcAg4AmlVJv/LEipm5VSa5RSa9LTfafTfSGEEKcmNCSMhyOu5oZDu9n0/cdmx3E6VxX0ZCC+wv2mQMpx5pmjtS7QWmcAi4EulRektX5fa91da909Nja2zgILIYTwPl0uvp3dfzSg8J03zI7idK4q6KuB1kqp5kqpAGAU8FOleX4E+iql/JRSIUBPYIuL8gkhhPABwaHhbBjZmUcv1mzY+KXZcZzKJQVda10OjAfmYhTpr7XWm5RStyqlbnXMswWYA2wAVgFTtdYbXZFPCCGE77jozne5X5XQYd23ZkdxKpddXa+1ng3MrvTYlEr3JwITXZVJCCGE7wkJiaFro1GkffwJBaGf0/rSMWZHcgrp+lUIIYTPCTz7RtIPhfDb/FfNjuI0UtCFEEL4nMimiXx9WyumdC9j0dofzY7jFFLQhRBC+KSbh75OsN3O94teNDuKU0hBF0II4ZMSG7fh+vXR3DA1h1W/fW52nFMmBV0IIYTPGnDNBH7qrZiz/0Ozo5wyKehCCCF8Vtuu/bEMasH31lRSUtaYHeeUSEEXQgjh067rO4E2yZpZL95pdpRTIgVdCCGET2sU15UR6wNovyKbLdtWmR3npElBF0II4fOa3fcM995sYeZizx1aVQq6EEIIn3dmr2E8VtiS/9u/gsMHksyOc1KkoAshhBBAl3MfI31eOHsevc3sKCdFCroQQggBND+tJzsTovkmZi+5OfvNjlNrUtCFEEIIh/hnnsS/eRGla6aZHaXWpKALIYQQDu3aXMzjYWegv5xGXmqK2XFqRQq6EEIIUcGekIvIWBLE/BdvMTtKrUhBF0IIISpoP/I6Ph0RwOsdd5Gdl2F2nBqTgi6EEEJU0q3/TWQGWHnnpwfMjlJjUtCFEEKISi4fcBvDN8Np01aQn5NpdpwakYIuhBBCVGKxWunRaAB2O/w6+1Gz49SIn9kBhBBCCHc09K43GFOvGzlFy7i0rBg//yCzI1VJ9tCFEEKI47BYrdzc7irSbZqvPr7b7DjVkoIuhBBCnMA5Pf+PJ7+x03jaYspKS8yOUyUp6EIIIcQJWK3+5F/Qi8kXWflo9jNmx6mSFHQhhBCiCiPuepdeoXa6b5qNttvNjnNCUtCFEEKIKgQEBHJO45tI+CuDDe+8aHacE5KCLoQQQlSjy0U3cSgpjG2rv3TbvXQp6EIIIUQ1AkLD2PrUQKb2Kydj+89mxzkuKehCCCFEDVwy6GVmZWv8fn3b7CjHJQVdCCGEqAH/gFC2lg8i9YNkVk6baHac/5CCLoQQQtRQixseY1lnxSfpn5sd5T+koAshhBA1FBbTgH0XdmZJw3J+XTbd7DjHkIIuhBBC1MJtF71Kywwb22e8ZnaUY0hBF0IIIWqhUUw8ozZFc87iEtYv/8LsOEdJQRdCCCFqqd8T7/DgLRZm7JpidpSjpKALIYQQtdS4eWeGNG7H3PLDbNzyu9lxACnoQgghxEkZ3fc57vzJztbHHzA7CiAFXQghhDgpDRu0J6heGJujS/lr6xKz40hBF0IIIU5W18cmsaW7jR3z3jI7ihR0IYQQ4mR1bNWDe0p7MnjTElL/+cvULFLQhRBCiFPQpPetpCyIZNPE/zM1hxR0IYQQ4hQ07X4Wf1xZnyf7ZJCfnWRaDinoQgghxCm67PpX+DAjjeDV00zLIAVdCCGEOEVNEs4m2NabpOc+I3PPLlMySEEXQgghnKC461VkFPnx8ZfjTVm/FHQhhBDCCdoMvZLJ14cxs+E+Ug8fcPn6paALIYQQTnJlp7vIV4rPPrnD5euWgi6EEEI4yZA+V/PQL9Dns21kpSe7dN0uK+hKqcFKqW1KqZ1KqYePM72/UipHKbXOcXvSVdmEEEIIZ2lwyUimXmBh9qrnXLpelxR0pZQVmAxcCHQARiulOhxn1iVa69Mdt2ddkU0IIYRwpvPHPklZu2A+Sl1KaUmey9brqj30HsBOrfVurXUp8CUw3EXrFkIIIVzq+nbXUVYI38x5xGXrdFVBbwLsr3A/2fFYZb2VUuuVUr8qpTq6JpoQQgjhXH173EbT2IbMtqS5bJ1+LlqPOs5jutL9v4BErXW+UmoI8APQ+j8LUupm4GaAhIQEJ8cUQgghTp2yWHh5yMfEBse6bJ2u2kNPBuIr3G8KpFScQWudq7XOd/w9G/BXSsVUXpDW+n2tdXetdffYWNe9UUIIIURtxIfHE+QX5LL1uaqgrwZaK6WaK6UCgFHATxVnUEo1Ukopx989HNkOuyifEEII4dFc0uSutS5XSo0H5gJW4COt9Sal1K2O6VOAEcBtSqlyoAgYpbWu3CwvhBBCiONQnlwzu3fvrtesWWN2DCGEEMJllFJrtdbdKz8uPcUJIYQQXkAKuhBCCOEFpKALIYQQXkAKuhBCCOEFpKALIYQQXkAKuhBCCOEFpKALIYQQXkAKuhBCCOEFpKALIYQQXkAKuhBCCOEFpKALIYQQXkAKuhBCCOEFpKALIYQQXkAKuhBCCOEFpKALIYQQXsCjx0NXSqUDSU5cZAyQ4cTleTp5P44l78e/5L04lrwfx5L341918V4kaq1jKz/o0QXd2ZRSa443aLyvkvfjWPJ+/Evei2PJ+3EseT/+5cr3QprchRBCCC8gBV0IIYTwAlLQj/W+2QHcjLwfx5L341/yXhxL3o9jyfvxL5e9F3IMXQghhPACsocuhBBCeAGfLOhKqcFKqW1KqZ1KqYePM10ppd5yTN+glOpmRk5XqcH70V8plaOUWue4PWlGTldQSn2klEpTSm08wXRf2zaqez98aduIV0otUEptUUptUkrdfZx5fGL7qOF74UvbRpBSapVSar3j/XjmOPPU/bahtfapG2AFdgEtgABgPdCh0jxDgF8BBfQCVpqd2+T3oz8wy+ysLno/+gHdgI0nmO4z20YN3w9f2jbigG6Ov8OB7b763VHD98KXtg0FhDn+9gdWAr1cvW344h56D2Cn1nq31roU+BIYXmme4cCn2rACiFRKxbk6qIvU5P3wGVrrxUBmFbP40rZRk/fDZ2itD2qt/3L8nQdsAZpUms0nto8avhc+w/F55zvu+jtulU9Qq/NtwxcLehNgf4X7yfx3Q6zJPN6ipq+1t6M56VelVEfXRHNLvrRt1JTPbRtKqWZAV4w9sYp8bvuo4r0AH9o2lFJWpdQ6IA34XWvt8m3Dz5kL8xDqOI9V/iVVk3m8RU1e618YXQ3mK6WGAD8Ares6mJvypW2jJnxu21BKhQHfAvdorXMrTz7OU7x2+6jmvfCpbUNrbQNOV0pFAt8rpTpprSuee1Ln24Yv7qEnA/EV7jcFUk5iHm9R7WvVWuceaU7SWs8G/JVSMa6L6FZ8aduolq9tG0opf4wCNkNr/d1xZvGZ7aO698LXto0jtNbZwEJgcKVJdb5t+GJBXw20Vko1V0oFAKOAnyrN8xNwteOsxF5Ajtb6oKuDuki174dSqpFSSjn+7oGx3Rx2eVL34EvbRrV8adtwvM4PgS1a69dPMJtPbB81eS98bNuIdeyZo5QKBgYCWyvNVufbhs81uWuty5VS44G5GGd4f6S13qSUutUxfQowG+OMxJ1AIXCdWXnrWg3fjxHAbUqpcqAIGKUdp216G6XUFxhn58YopZKBpzBOcPG5bQNq9H74zLYBnA2MA/5xHCsFeBRIAJ/bPmryXvjSthEHfKKUsmL8cPlaaz3L1XVFeooTQgghvIAvNrkLIYQQXkcKuhBCCOEFpKALIYQQXkAKuhBCCOEFpKALIYQQXkAK+ilQSjVTSmmllJ/j/q9KqWvMznWEUqqvUmqbC9bztFLqs1rMr5VSrRx/T1FKPVF36eqWUuo2pVSqUipfKVXf7DyuopT6WCn1nBvk6O+4nE4In+dz16HXJa31hWZnqEhrvQRoa3aOqmitb63JfEqpvcCNWus/6jZRzTl6ynodY1Sl9WbnEUL4NtlDF+LkNQSCgE3Hm3ik5Ua4J/l8hLfxyoKulNqrlLrfMYh8jlLqK6VUUIXpNyljkPlMpdRPSqnGFaZppdStSqkdSqkspdTkCt0XWpVSryqlMpRSu4GLKq13oVLqRsff1yqlliml3lBKZSuldiulznI8vl8plVaxeV4pFehY9j5HE+4URxeCR5sVlVL3OZ53UCl1XYXnDlFKbVZK5SmlDiil7q/4vArztXdkzFZKbVJKDasw7WPHa/3FsZyVSqmWFab/z5E7Vym1VinVtxafxwOOzClKqesrTTvadKuUilFKzXLky1RKLVFKWZRS0zF6oPrZ0bT9oGP+b5RShxyf8WJVYTSnGryejkqp3x3rSVVKPep43KKUelgptUspdVgp9bVSKvo4r6kNcORwRrZSar7jca2UukMptQPY4Xisuu3tdsf2lqeUmqCUaqmUWu54r79WRpe8x3tfa7uNXaSU+tux3P1KqacrTDty+Ohmx+d0UCl1XzUfbYzjPcxTSi1SSiVWWN5ZSqnVjs9mtVLqrArT9iqlBla4f/SQTYUc1yjj/0KGUuqxCvMGOz7bLKXUZuDMSu/Jkc8uTxn/Jy49wfuVCUxwfCanVZingVKqSCkVW81rF8L9OHuAdXe4AXuBVUBjIBpjrN5bHdPOBTKAbkAg8DawuMJzNTALiMQoIunAYMe0WzH65413LHeBY34/x/SFGM3CANcC5Rjd+1mB54B9wGTHei8A8oAwx/xvYvT1Gw2EAz8DLzqm9Xcs61mMbjeHYHQdGOWYfhDo6/g7CuhW4XnJjr/9MbocfBQIcLwPeUBbx/SPMca97oFxKGYG8GWF92UsUN8x7T7gEBDkmPY08NkJPovBQCrQCQgFPne8Z60qrPc5x98vAlP4dzzhvvzbm+FeYGClZV/veK8CHe/fugrTTvh6HM856HgdQY77PR3T7gFWYAycEAi8B3xxgtfWjAqff4Xt53fH5xhMzba3n4AIoCNQAswDWgD1gM3ANSdY/7XUbhvrD5yG8UO+s+NzuaTSa/nC8TmdhrHtDzzBuj92LLufY13/A5Y6pkUDWRhdg/oBox336x/vs6TC9lMhxweO96+L4z1p75j+ErDEsY54YCOObdwx/QqM//cW4EqgAIir9H7d6cgVDLwDvFzh+XcDP5v9HSY3uZ3MzfQAdfKijC+MsRXuvwJMcfz9IfBKhWlhQBnQzHFfA30qTP8aeNjx93wcPwwc9y+g6oK+o8K8pznmbVjhscPA6RjD6hUALStM6w3scfzdH6Mv5IqFIw3j2C0YX+K3ABGV3of+/FvQ+2IUYUuF6V8ATzv+/hiYWmHaEGBrFe9xFtDF8ffRL+TjzPcR8FKF+204cUF/FvjxyLTjfKbHLS6O6ZGO5dar7vVgFJi/T7CcLcB5Fe7HObYPv+PM24zjF/RzK9yvyfZ2doXpa4GHKtx/DXjzBFlrvI2d4PlvAm9Uei3tKv2/+fAEz/2YY3/whQE2jCI7DlhVaf7lwLXH+yw5fkFvWmH6Kox+wAF24/iB7bh/MxUK+nFyrgOGV3i/9lWa3hNjjGqL4/4aYOSJlic3ubnzzSub3B0OVfi7EOMLB4xf70lHJmhjeL/DHDvQfFXPrThAfRJVS63wd5FjfZUfCwNigRBgraPpNBuY43j8iMNa6/IT5Loco2AlOZo+ex8nS2Ngv9baXil/TV43ymju3+JoQs3G2HusyVCItXnPJmK0IvzmaD5++EQzKuPwx0uO5tVcjCJBpUwnej3xwK4TLDoRYyzjI5/DFoxC1bCK3JVVfL012d4qbxPH20ZOpKbbGEqpnkqpBUqpdKVUDkaLU+XPsPJn1ZgTOzqv43VlOuY/5jVXWFYTau6k/g8qpa5WSq2r8Pl14tjXWPG5aK1XYvyYPkcp1Q5oxX9HXxTCI3hzQT+RFIwvbQCUUqEYTckHavDcgxw7nm2CkzJlYHzxdtRaRzpu9bTWVX2RH6W1Xq21Hg40AH7AaFWoLAWIV0pV/MwTqMHrVsbx8oeAkRjN/JFADkbLQnVq/J5prfO01vdprVsAFwP3KqXOOzK50uxjgOEYwxTWw9izo4aZ9gMtq5h2YYXPIVJrHaS1rsn2cfSlVPj7VLY3Z/sco1jFa63rYRzeqPx+Vf6sqhqv+ei8SqkwjGbwFCq95grLOvKaCzB+wB7RqIb5oYrtyXEM/wNgPEbzfiRGk3zF11h5OwL4BOOQ0jhgpta6uBZ5hHAbvljQPweuU0qdrpQKBF4AVmqt99bguV8DdymlmiqlooAT7kHWhmOv+QPgDaVUAwClVBOl1KDqnquUClBKXaWUqqe1LgNyMfYoKzuyJ/KgUspfKdUfo2h+WYOI4RjHHtMBP6XUkxjHfGvia+BapVQHpVQIxvCbJ3otQ5VSrZRSqsLrOPJaUjGOK1fMVIKxtxuC8TnW1CygkVLqHmWcjBiulOrpmDYFeP7ICV7KGOd4eC2WXdmpbG/OFg5kaq2LlTE+9ZjjzPOEUipEGScYXgd8VcXyhiil+ijjpL0JGK9rP8YwkW2UUmOUUn5KqSuBDhjvOxjN4KMc22F3jGE2a+pr4BGlVJRSqinG8fAjQjEKdjqAMk4c7VSDZU4HLsUo6p/WIosQbsXnCrrWeh7wBPAtxq/9lsCoGj79A4xxw9cDfwHfOTHaQxjNzSscTch/UPNryMcBex3PuxXji+kYWutSYBhwIUaLwDvA1VrrrTVY/lzgV2A7RhNnMZWaLk9Ea/0rxrHa+Rivb34Vs7fGeN35GMdc39FaL3RMexF43NGUej/GF28Sxl7fZowT2WpEa50HnI/xg+YQxtnoAxyT/4exF/ubUirPsdyex1tODdd1Ktubs90OPOt4XU9y/JacRRif0zzgVa31b1Us73OMH2iZwBnAVQBa68PAUIyTDg8DDwJDtdYZjuc9gfE+ZAHPOJZTU89gfO57gN8wijGO9W7GOOdgOcYPwNOAZdUtUGudjPH/WWOccCeER5Lx0IUQKKWaYRRJ/0rnavgEpdRHQIrW+nGzswhxsqRjBSGET3P8mLkM6GpyFCFOic81uQshxBFKqQkYJ85N1FrvMTuPEKdCmtyFEEIILyB76EIIIYQXkIIuhBBCeAEp6EIIIYQXkIIuhBBCeAEp6EIIIYQXkIIuhBBCeIH/BzUY+GQji8eHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set(xlabel=\"nondimensional distance from map boundary                                          \", ylabel=\"tractUse\")\n",
    "plt.plot(yCenter,yUseHD1,linestyle=\"dashed\",label=\"method 1\")\n",
    "plt.plot(yCenter,yUseHD2,label=\"method 2\")\n",
    "idealX = [0,2,3]\n",
    "idealY = [1,1,0.5]\n",
    "plt.plot(idealX,idealY,linestyle=\"dashdot\")\n",
    "plt.plot(yCenter,yUseHD0, linestyle=\"dotted\",label=\"square HDs\")\n",
    "#plt.xlim((0,2))\n",
    "plt.legend(loc=10,fontsize=12)\n",
    "plt.rc('axes', labelsize=12)    # fontsize of the x and y labels\n",
    "plt.rcParams[\"figure.figsize\"] = (8,8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "67f9b138-69f8-4347-9ab0-e9a91a6d0bbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#this block - overcome my inability to suppress plotting for y* > 2\n",
    "plotHD0 = []\n",
    "plotHD1 = []\n",
    "plotHD2 = []\n",
    "plotyCenter = []\n",
    "for s in range(ySlices):\n",
    "    if yCenter[s] <= 2.0:\n",
    "        plotyCenter.append(yCenter[s])\n",
    "        plotHD0.append(yUseHD0[s])\n",
    "        plotHD1.append(yUseHD1[s])\n",
    "        plotHD2.append(yUseHD2[s])\n",
    "fig, ax = plt.subplots()\n",
    "ax.set(xlabel=\"nondimensional distance from map boundary \", ylabel=\"tractUse\")\n",
    "plt.plot(plotyCenter,plotHD1,linestyle=\"dashed\",label=\"method 1\")\n",
    "plt.plot(plotyCenter,plotHD2,label=\"method 2\")\n",
    "idealX = [0.1,2.05]\n",
    "idealY = [1,1]\n",
    "plt.plot(idealX,idealY,linestyle=\"dashdot\")\n",
    "plt.plot(plotyCenter,plotHD0, linestyle=\"dotted\",label=\"square HDs\")\n",
    "#plt.xlim((0,2))\n",
    "plt.legend(loc=0,fontsize=12)\n",
    "plt.rc('axes', labelsize=12)    # fontsize of the x and y labels\n",
    "plt.rcParams[\"figure.figsize\"] = (8,8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "0f1b9521-9080-4786-a409-8b95c6c40396",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def areaError(XLENGTH, L, nHA, targetArea ):\n",
    "    \"\"\"\n",
    "    This function calculates the mean-squared-error for wedge radius near a boundary to hit target area\n",
    "    The PROXIMITY is the distance from the edge of the map, HALFANGLE is half the included angle of the triangle\n",
    "    \"\"\"\n",
    "    origin = Point(0,L)\n",
    "    SEpt = Point(0. + XLENGTH, L - XLENGTH * math.tan(nHA))\n",
    "    NEpt = Point(0. + XLENGTH, L + XLENGTH * math.tan(nHA))\n",
    "    triPoly = Polygon([origin, SEpt, NEpt])\n",
    "    mapPoly = Polygon([Point(-50,0), Point(50,0), Point(50,50), Point(-50,50) ] )\n",
    "    calcArea = triPoly.intersection(mapPoly).area\n",
    "    totalError = (calcArea - targetArea)**2\n",
    "    return totalError\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "1d4ebd65-2d55-4935-b0ab-d9f6710977b3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5748245901332492 1.0000008464673829 1.0\n",
      "7.165070302347404e-13\n"
     ]
    }
   ],
   "source": [
    "L = 0.99\n",
    "nHA = 0.122*pi\n",
    "targetArea = 1.\n",
    "XLENGTH = 1.1\n",
    "root = minimize(areaError,[XLENGTH],args=(L, nHA, targetArea))\n",
    "xL = root.x[0]\n",
    "trueArea = xL*xL*tan(nHA)\n",
    "print(xL, trueArea, targetArea)\n",
    "print(areaError(xL, L, nHA, targetArea))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "2deadc0c-eb8b-431a-90c2-72bf7ee2afc4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS error is 0.049814 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.6\n",
      "RMS error is 0.047487 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.6\n",
      "RMS error is 0.04467 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.6\n",
      "RMS error is 0.041583 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.6\n",
      "RMS error is 0.055677 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.7\n",
      "RMS error is 0.055274 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.7\n",
      "RMS error is 0.055205 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.7\n",
      "RMS error is 0.055755 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.7\n",
      "RMS error is 0.087116 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.8\n",
      "RMS error is 0.088171 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.8\n",
      "RMS error is 0.089913 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.8\n",
      "RMS error is 0.092502 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# July 2023 -- NEW APPROACH - if a wedge underdelivers, we widen the wedge up to a max angle to make up the take,\n",
    "#   the opposite wedge's angle is also widened, and its take is capped as min wedge's take (HD2)\n",
    "# if a wedge _nearly_ underdelivers, run it to boundary, reduce ADJACENT wedges' take\n",
    "#  (this code has boundary on south edge.  If multi-constrained, need additional logic)\n",
    "\n",
    "#  simplistic version of \"HD2\" approach -- simply widen angles facing near-boundary edges\n",
    "maxAngle = [0.6*pi, 0.7*pi, 0.8*pi]\n",
    "param = [0.2, 0.3, 0.4, 0.5]   #this \"param\" is the min uncaptured wedge area near a boundary that we will not capture\n",
    "nParam = len(param)\n",
    "RMSE3 = [0.]*nParam\n",
    "ySlices = 4*100    #divide the latitudes into 2*1000 slices\n",
    "maxY = 4.\n",
    "dy = maxY/ySlices\n",
    "yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "for yy in range(ySlices):\n",
    "    yMin = dy*yy\n",
    "    yMax = dy*(yy+1.)\n",
    "    yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "    yCenter[yy]=yLayer[yy].centroid.y\n",
    "dummyPoly = Polygon([(0,0),(1,0),(1,1)])\n",
    "MAP = Polygon([(-99,0),(99,0),(99,99),(-99,99)])\n",
    "dx2 = [-1., 1., 1., -1.]  #these are the differences in x- and y-coordinate from the centerpoint for the 2nd and 3rd point in each wedge\n",
    "dx3 = [1., 1., -1., -1.]\n",
    "dy2 = [-1., -1., 1., 1.]\n",
    "dy3 = [-1., 1., 1., -1.]\n",
    "wedgePoly, maxPoly = [dummyPoly]*4, [dummyPoly]*4  #wedge poly is the actual wedge shape, maxPoly is this shape extended beyond boundary\n",
    "wedgePt2, wedgePt3, maxPt2, maxPt3 = [Point(0,0)]*4, [Point(0,0)]*4, [Point(0,0)]*4, [Point(0,0)]*4 #2nd & 3rd pt vertices\n",
    "maxArea = [0.]*4\n",
    "for ii, A in enumerate(maxAngle):\n",
    "    for i,p in enumerate(param):\n",
    "        yUse = [0.]*ySlices   #akin to tractUse in HD code\n",
    "        for yy in range(ySlices):\n",
    "            wedgeAngle = [0.5*pi]*4  #reset these angles from last round\n",
    "            wedgeR = [2.**0.5]*4         #wedge radius, default = sqrt(2) so triangular areas are unity\n",
    "            neededWedgeArea = 1. #default\n",
    "            nWA = [neededWedgeArea]*4\n",
    "            L = (0.5+yy)*dy    #height of centerpoint above the boundary for this loop\n",
    "            CP = Point(0,L)  #centerpoint\n",
    "            for w in range(4):\n",
    "                maxPt2 = Point(CP.x + 10.*dx2[w], CP.y + 10.*dy2[w])\n",
    "                maxPt3 = Point(CP.x + 10.*dx3[w], CP.y + 10.*dy3[w]) \n",
    "                maxPoly[w] = Polygon([CP, maxPt2, maxPt3]) \n",
    "                maxArea[w] = maxPoly[w].intersection(MAP).area\n",
    "                #plotPoly(maxPoly[w])\n",
    "                #plotCenter(w,maxPoly[w])\n",
    "            #plt.show()\n",
    "\n",
    "            minW = maxArea.index(np.min(maxArea))   #index of the short wedge (always 0 in this 1-edge map)\n",
    "            #print(\"min wedge no, min max Area are\",minW, maxArea[minW])\n",
    "            wHA, nHA = pi/4., pi/4.  #default wide and narrow half-angles\n",
    "            if np.min(maxArea) < neededWedgeArea:  #we have a short wedge. First, check if we can fix by widening angle\n",
    "                idealX = neededWedgeArea / L\n",
    "                wideAngle = 2.*math.atan(idealX / L)\n",
    "                if wideAngle > maxAngle[ii]:\n",
    "                    wideAngle = maxAngle[ii]\n",
    "                narrowAngle = pi - wideAngle\n",
    "                wedgeAngle = [wideAngle, narrowAngle, wideAngle, narrowAngle]\n",
    "\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * narrowAngle  #narrowHalfAngle      \n",
    "                southX = L*tan(wHA)   #max x for the south triangle within the map\n",
    "                southArea = L * southX\n",
    "                targetArea = 0.5* (4.*neededWedgeArea - 2.*southArea)  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                guessed_XLENGTH = 2.\n",
    "                root = minimize(areaError,[guessed_XLENGTH],args=(L, nHA, targetArea))\n",
    "                eastdX = root.x[0]\n",
    "                eastHalfY = eastdX * tan(nHA)\n",
    "                wedgeR[1] = (eastdX*eastdX + eastHalfY*eastHalfY)**0.5\n",
    "                #print(\"wedgeR[1] =\",round(wedgeR[1],5) )\n",
    "\n",
    "                #northeastPoint = Point(southX, 2.*L)\n",
    "                #southeastPoint = Point(southX, 0.)\n",
    "                #eastTriangle = Polygon([ CP,southeastPoint,northeastPoint ])\n",
    "                #eastNeededArea = eastNeededArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                #a = 0.5 * tan(nHA)\n",
    "                #b = 2.*L                  \n",
    "                #c = -1.*eastNeededArea\n",
    "                #eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                wedgeR = [L/cos(wHA), eastdX/cos(nHA), L/cos(wHA), eastdX/cos(nHA)]\n",
    "                #print(\"eastdX, wedge Rs are\",round(eastdX,5),wedgeR)\n",
    "\n",
    "            elif np.min(maxArea) - neededWedgeArea < p * neededWedgeArea :   #we are close enough to edge to leave a constrained remnant.  Pick it up.\n",
    "                areaGlut = maxArea[minW] - neededWedgeArea\n",
    "                reducedNeededWedgeArea = neededWedgeArea - areaGlut / 2.  #two adj wedges shrink to accommodate.  For 1-edge, none will hit edge\n",
    "                for w in [int((minW+1)%4), int((minW+3)%4) ] :\n",
    "                    wedgeR[w] = (2.*reducedNeededWedgeArea) ** 0.5  #note: in this case, we are not changing wedge angles.  \"2\" from triangle\n",
    "                wedgeR[minW] = 10.  #this one is unconstrained, to get to boundary\n",
    "\n",
    "            startAngle = [-0.5*pi-wHA, 0.*pi-nHA, 0.5*pi-wHA, 1.*pi-nHA]\n",
    "            stopAngle =  [-0.5*pi+wHA, 0.*pi+nHA, 0.5*pi+wHA, 1.*pi+nHA]\n",
    "            for w in range(4):\n",
    "                wedgePt2 = Point(CP.x + wedgeR[w] * math.cos(startAngle[w]), CP.y + wedgeR[w] * math.sin(startAngle[w]) )\n",
    "                wedgePt3 = Point(CP.x + wedgeR[w] * math.cos(stopAngle[w]),  CP.y + wedgeR[w] * math.sin(stopAngle[w])  )   \n",
    "                wedgePoly[w] = Polygon([CP, wedgePt2, wedgePt3])\n",
    "\n",
    "            finalPoly = wedgePoly[0].union(wedgePoly[1].union(wedgePoly[2].union(wedgePoly[3]) )  )\n",
    "            if abs(finalPoly.intersection(MAP).area - 4.) > 0.1:\n",
    "                print(\"error!  final Poly area is\", finalPoly.intersection(MAP).area,\"not 4.00\")\n",
    "                pause = input(\"click to stop\")\n",
    "            if yy%50 == -1 :  #0 ; impossible:\n",
    "                print(\"L, areaGlut, wedgeRs are\",L,r5(areaGlut), wedgeR)\n",
    "                print(\"L,finalPoly-MAP area = \",round(L,3),round(finalPoly.intersection(MAP).area,4))  #debug, should equal 2\n",
    "                #plotPoly(finalPoly)\n",
    "                plotPoly(Polygon([Point(-1,0), Point(1,0), Point(1,2), Point(-1,2)]) )           \n",
    "                for w in range(4):\n",
    "                    print(\"wedge no, area \",w, round((wedgePoly[w].intersection(MAP)).area, 5) ) \n",
    "                    plotPoly(wedgePoly[w])\n",
    "                plt.show()\n",
    "                pause = input(\"ready to continue?\")\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE3[i] = round(variance **0.5,6)\n",
    "        MAXA = r3(maxAngle[ii]/pi)\n",
    "        print(\"RMS error is\",RMSE3[i],\"for max extra-captured relative wedge area of\",p,\"and maxAngle/pi=\",MAXA )\n",
    "        plt.plot(yCenter,yUse,label=\"max uncap = \"+str(p)+\", maxA/pi=\"+str(MAXA) )\n",
    "plt.xlabel(\"distance from edge\")\n",
    "plt.ylabel(\"relative layer use\")\n",
    "plt.legend(loc=1)\n",
    "plt.title(\"yUse vs. max extra-captured wedge area\" )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "3a06d9d0-00ad-4be5-90be-f383fc819507",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.0, 0.9974906014594823, 1.0, 0.9974906014594823]\n",
      "[1.57079632675, 1.57079632675, 1.57079632675, 1.57079632675]\n",
      "[-2.356194490125, -0.785398163375, 0.785398163375, 2.356194490125]\n",
      "[-0.785398163375, 0.785398163375, 2.356194490125, 3.926990816875]\n",
      "0.785398163375 0.785398163375 0.25\n"
     ]
    }
   ],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "a03c6967-9e0f-49f8-8a43-bf5ea42b962d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Repeat of above, but with the nonlinear rule for angle vs. L*\n",
      "RMS error is 0.055285 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.6\n",
      "RMS error is 0.05253 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.6\n",
      "RMS error is 0.049005 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.6\n",
      "RMS error is 0.044796 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.6\n",
      "RMS error is 0.035844 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.7\n",
      "RMS error is 0.032881 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.7\n",
      "RMS error is 0.029192 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.7\n",
      "RMS error is 0.024974 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.7\n",
      "RMS error is 0.018415 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.8\n",
      "RMS error is 0.015267 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.8\n",
      "RMS error is 0.011739 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.8\n",
      "RMS error is 0.00895 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Repeat of above, but with the nonlinear rule for angle vs. L*\")\n",
    "levelY = 0.36\n",
    "maxWt = 1.9\n",
    "maxAngle = [0.6*pi, 0.7*pi, 0.8*pi]\n",
    "param = [0.2, 0.3, 0.4, 0.5]   #this \"param\" is the min uncaptured wedge area near a boundary that we will not capture\n",
    "nParam = len(param)\n",
    "RMSE3 = [0.]*nParam\n",
    "ySlices = 4*100    #divide the latitudes into 2*1000 slices\n",
    "maxY = 4.\n",
    "dy = maxY/ySlices\n",
    "yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "for yy in range(ySlices):\n",
    "    yMin = dy*yy\n",
    "    yMax = dy*(yy+1.)\n",
    "    yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "    yCenter[yy]=yLayer[yy].centroid.y\n",
    "dummyPoly = Polygon([(0,0),(1,0),(1,1)])\n",
    "MAP = Polygon([(-99,0),(99,0),(99,99),(-99,99)])\n",
    "dx2 = [-1., 1., 1., -1.]  #these are the differences in x- and y-coordinate from the centerpoint for the 2nd and 3rd point in each wedge\n",
    "dx3 = [1., 1., -1., -1.]\n",
    "dy2 = [-1., -1., 1., 1.]\n",
    "dy3 = [-1., 1., 1., -1.]\n",
    "wedgePoly, maxPoly = [dummyPoly]*4, [dummyPoly]*4  #wedge poly is the actual wedge shape, maxPoly is this shape extended beyond boundary\n",
    "wedgePt2, wedgePt3, maxPt2, maxPt3 = [Point(0,0)]*4, [Point(0,0)]*4, [Point(0,0)]*4, [Point(0,0)]*4 #2nd & 3rd pt vertices\n",
    "maxArea = [0.]*4\n",
    "for ii, A in enumerate(maxAngle):\n",
    "    for i,p in enumerate(param):\n",
    "        yUse = [0.]*ySlices   #akin to tractUse in HD code\n",
    "        for yy in range(ySlices):\n",
    "            wedgeAngle = [0.5*pi]*4  #reset these angles from last round\n",
    "            wedgeR = [2.**0.5]*4         #wedge radius, default = sqrt(2) so triangular areas are unity\n",
    "            neededWedgeArea = 1. #default\n",
    "            nWA = [neededWedgeArea]*4\n",
    "            L = (0.5+yy)*dy    #height of centerpoint above the boundary for this loop\n",
    "            CP = Point(0,L)  #centerpoint\n",
    "            for w in range(4):\n",
    "                maxPt2 = Point(CP.x + 10.*dx2[w], CP.y + 10.*dy2[w])\n",
    "                maxPt3 = Point(CP.x + 10.*dx3[w], CP.y + 10.*dy3[w]) \n",
    "                maxPoly[w] = Polygon([CP, maxPt2, maxPt3]) \n",
    "                maxArea[w] = maxPoly[w].intersection(MAP).area\n",
    "                #plotPoly(maxPoly[w])\n",
    "                #plotCenter(w,maxPoly[w])\n",
    "            #plt.show()\n",
    "\n",
    "            minW = maxArea.index(np.min(maxArea))   #index of the short wedge (always 0 in this 1-edge map)\n",
    "            #print(\"min wedge no, min max Area are\",minW, maxArea[minW])\n",
    "            wHA, nHA = pi/4., pi/4.  #default wide and narrow half-angles\n",
    "            if np.min(maxArea) < neededWedgeArea:  #we have a short wedge. First, check if we can fix by widening angle\n",
    "                weight = max(1.0,1.0 + (levelY - L)/(levelY - 0.)*(maxWt-1.0) )\n",
    "                wideAngle = min(maxAngle[ii],pi/2.*weight)\n",
    "                idealX = neededWedgeArea / L\n",
    "                #wideAngle = 2.*math.atan(idealX / L)\n",
    "                if wideAngle > maxAngle[ii]:\n",
    "                    wideAngle = maxAngle[ii]\n",
    "                narrowAngle = pi - wideAngle\n",
    "                wedgeAngle = [wideAngle, narrowAngle, wideAngle, narrowAngle]\n",
    "\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * narrowAngle  #narrowHalfAngle      \n",
    "                southX = L*tan(wHA)   #max x for the south triangle within the map\n",
    "                southArea = L * southX\n",
    "                targetArea = 0.5* (4.*neededWedgeArea - 2.*southArea)  #this is for EAST and WEST wedges only -- we will short north also\n",
    "                guessed_XLENGTH = 2.\n",
    "                root = minimize(areaError,[guessed_XLENGTH],args=(L, nHA, targetArea))\n",
    "                eastdX = root.x[0]\n",
    "                eastHalfY = eastdX * tan(nHA)\n",
    "                wedgeR[1] = (eastdX*eastdX + eastHalfY*eastHalfY)**0.5\n",
    "                #print(\"wedgeR[1] =\",round(wedgeR[1],5) )\n",
    "\n",
    "                #northeastPoint = Point(southX, 2.*L)\n",
    "                #southeastPoint = Point(southX, 0.)\n",
    "                #eastTriangle = Polygon([ CP,southeastPoint,northeastPoint ])\n",
    "                #eastNeededArea = eastNeededArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                #a = 0.5 * tan(nHA)\n",
    "                #b = 2.*L                  \n",
    "                #c = -1.*eastNeededArea\n",
    "                #eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                wedgeR = [L/cos(wHA), eastdX/cos(nHA), L/cos(wHA), eastdX/cos(nHA)]\n",
    "                #print(\"eastdX, wedge Rs are\",round(eastdX,5),wedgeR)\n",
    "\n",
    "            elif np.min(maxArea) - neededWedgeArea < p * neededWedgeArea :   #we are close enough to edge to leave a constrained remnant.  Pick it up.\n",
    "                areaGlut = maxArea[minW] - neededWedgeArea\n",
    "                reducedNeededWedgeArea = neededWedgeArea - areaGlut / 2.  #two adj wedges shrink to accommodate.  For 1-edge, none will hit edge\n",
    "                for w in [int((minW+1)%4), int((minW+3)%4) ] :\n",
    "                    wedgeR[w] = (2.*reducedNeededWedgeArea) ** 0.5  #note: in this case, we are not changing wedge angles.  \"2\" from triangle\n",
    "                wedgeR[minW] = 10.  #this one is unconstrained, to get to boundary.  oppWedge radius is not modified\n",
    "\n",
    "            startAngle = [-0.5*pi-wHA, 0.*pi-nHA, 0.5*pi-wHA, 1.*pi-nHA]\n",
    "            stopAngle =  [-0.5*pi+wHA, 0.*pi+nHA, 0.5*pi+wHA, 1.*pi+nHA]\n",
    "            for w in range(4):\n",
    "                wedgePt2 = Point(CP.x + wedgeR[w] * math.cos(startAngle[w]), CP.y + wedgeR[w] * math.sin(startAngle[w]) )\n",
    "                wedgePt3 = Point(CP.x + wedgeR[w] * math.cos(stopAngle[w]),  CP.y + wedgeR[w] * math.sin(stopAngle[w])  )   \n",
    "                wedgePoly[w] = Polygon([CP, wedgePt2, wedgePt3])\n",
    "\n",
    "            finalPoly = wedgePoly[0].union(wedgePoly[1].union(wedgePoly[2].union(wedgePoly[3]) )  )\n",
    "            if abs(finalPoly.intersection(MAP).area - 4.) > 0.1:\n",
    "                print(\"error!  final Poly area is\", finalPoly.intersection(MAP).area,\"not 4.00\")\n",
    "                pause = input(\"click to stop\")\n",
    "            if yy%50 == -1 :  #0 ; impossible:\n",
    "                print(\"L, areaGlut, wedgeRs are\",L,r5(areaGlut), wedgeR)\n",
    "                print(\"L,finalPoly-MAP area = \",round(L,3),round(finalPoly.intersection(MAP).area,4))  #debug, should equal 2\n",
    "                #plotPoly(finalPoly)\n",
    "                plotPoly(Polygon([Point(-1,0), Point(1,0), Point(1,2), Point(-1,2)]) )           \n",
    "                for w in range(4):\n",
    "                    print(\"wedge no, area \",w, round((wedgePoly[w].intersection(MAP)).area, 5) ) \n",
    "                    plotPoly(wedgePoly[w])\n",
    "                plt.show()\n",
    "                pause = input(\"ready to continue?\")\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE3[i] = round(variance **0.5,6)\n",
    "        MAXA = r3(maxAngle[ii]/pi)\n",
    "        print(\"RMS error is\",RMSE3[i],\"for max extra-captured relative wedge area of\",p,\"and maxAngle/pi=\",MAXA )\n",
    "        plt.plot(yCenter,yUse,label=\"max uncap = \"+str(p)+\", maxA/pi=\"+str(MAXA) )\n",
    "plt.xlabel(\"distance from edge\")\n",
    "plt.ylabel(\"relative layer use\")\n",
    "plt.legend(loc=8)\n",
    "plt.title(\"yUse vs. max extra-captured wedge area with levelY, maxWt = \"+str(levelY)+\",\"+str(maxWt) )\n",
    "plt.show()  \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "3c1e3ee4-3451-4ef9-9b63-1b35c0fc8662",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Repeat of above, but allowing opp wedge to pick up some of slack\n",
      "RMS error is 0.057848 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.6\n",
      "RMS error is 0.054908 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.6\n",
      "RMS error is 0.051105 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.6\n",
      "RMS error is 0.046506 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.6\n",
      "RMS error is 0.038911 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.7\n",
      "RMS error is 0.0357 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.7\n",
      "RMS error is 0.031615 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.7\n",
      "RMS error is 0.026799 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.7\n",
      "RMS error is 0.021598 for max extra-captured relative wedge area of 0.2 and maxAngle/pi= 0.8\n",
      "RMS error is 0.018 for max extra-captured relative wedge area of 0.3 and maxAngle/pi= 0.8\n",
      "RMS error is 0.01358 for max extra-captured relative wedge area of 0.4 and maxAngle/pi= 0.8\n",
      "RMS error is 0.008926 for max extra-captured relative wedge area of 0.5 and maxAngle/pi= 0.8\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Repeat of above, but allowing opp wedge to pick up some of slack\")  #THIS SEEMS TO HARM LOW-l\n",
    "levelY = 0.36\n",
    "maxWt = 1.9\n",
    "oppWpickupFrac = 0.2\n",
    "maxAngle = [0.6*pi, 0.7*pi, 0.8*pi]\n",
    "param = [0.2, 0.3, 0.4, 0.5]   #this \"param\" is the min uncaptured wedge area near a boundary that we will not capture\n",
    "nParam = len(param)\n",
    "RMSE3 = [0.]*nParam\n",
    "ySlices = 4*100    #divide the latitudes into 2*1000 slices\n",
    "maxY = 4.\n",
    "dy = maxY/ySlices\n",
    "yCenter = [0.]*ySlices  #center latitude of each layer\n",
    "yLayer = [ Polygon([(0,0),(0,1),(1,1)]) ] *ySlices   #these are static layers for intersection checks\n",
    "for yy in range(ySlices):\n",
    "    yMin = dy*yy\n",
    "    yMax = dy*(yy+1.)\n",
    "    yLayer[yy]= Polygon([(0.,yMin),(999,yMin),(999,yMax),(0.,yMax)])\n",
    "    yCenter[yy]=yLayer[yy].centroid.y\n",
    "dummyPoly = Polygon([(0,0),(1,0),(1,1)])\n",
    "MAP = Polygon([(-99,0),(99,0),(99,99),(-99,99)])\n",
    "dx2 = [-1., 1., 1., -1.]  #these are the differences in x- and y-coordinate from the centerpoint for the 2nd and 3rd point in each wedge\n",
    "dx3 = [1., 1., -1., -1.]\n",
    "dy2 = [-1., -1., 1., 1.]\n",
    "dy3 = [-1., 1., 1., -1.]\n",
    "wedgePoly, maxPoly = [dummyPoly]*4, [dummyPoly]*4  #wedge poly is the actual wedge shape, maxPoly is this shape extended beyond boundary\n",
    "wedgePt2, wedgePt3, maxPt2, maxPt3 = [Point(0,0)]*4, [Point(0,0)]*4, [Point(0,0)]*4, [Point(0,0)]*4 #2nd & 3rd pt vertices\n",
    "maxArea = [0.]*4\n",
    "for ii, A in enumerate(maxAngle):\n",
    "    for i,p in enumerate(param):\n",
    "        yUse = [0.]*ySlices   #akin to tractUse in HD code\n",
    "        for yy in range(ySlices):\n",
    "            wedgeAngle = [0.5*pi]*4  #reset these angles from last round\n",
    "            wedgeR = [2.**0.5]*4         #wedge radius, default = sqrt(2) so triangular areas are unity\n",
    "            neededWedgeArea = 1. #default\n",
    "            nWA = [neededWedgeArea]*4\n",
    "            L = (0.5+yy)*dy    #height of centerpoint above the boundary for this loop\n",
    "            CP = Point(0,L)  #centerpoint\n",
    "            for w in range(4):\n",
    "                maxPt2 = Point(CP.x + 10.*dx2[w], CP.y + 10.*dy2[w])\n",
    "                maxPt3 = Point(CP.x + 10.*dx3[w], CP.y + 10.*dy3[w]) \n",
    "                maxPoly[w] = Polygon([CP, maxPt2, maxPt3]) \n",
    "                maxArea[w] = maxPoly[w].intersection(MAP).area\n",
    "                #plotPoly(maxPoly[w])\n",
    "                #plotCenter(w,maxPoly[w])\n",
    "            #plt.show()\n",
    "\n",
    "            minW = maxArea.index(np.min(maxArea))   #index of the short wedge (always 0 in this 1-edge map)\n",
    "            #print(\"min wedge no, min max Area are\",minW, maxArea[minW])\n",
    "            wHA, nHA = pi/4., pi/4.  #default wide and narrow half-angles\n",
    "            if np.min(maxArea) < neededWedgeArea:  #we have a short wedge. First, check if we can fix by widening angle\n",
    "                weight = max(1.0,1.0 + (levelY - L)/(levelY - 0.)*(maxWt-1.0) )\n",
    "                wideAngle = min(maxAngle[ii],pi/2.*weight)\n",
    "                idealX = neededWedgeArea / L\n",
    "                #wideAngle = 2.*math.atan(idealX / L)\n",
    "                if wideAngle > maxAngle[ii]:\n",
    "                    wideAngle = maxAngle[ii]\n",
    "                narrowAngle = pi - wideAngle\n",
    "                wedgeAngle = [wideAngle, narrowAngle, wideAngle, narrowAngle]\n",
    "\n",
    "                wHA = 0.5 * wideAngle  #wideHalfAngle\n",
    "                nHA = 0.5 * narrowAngle  #narrowHalfAngle      \n",
    "                southX = L*tan(wHA)   #max x for the south triangle within the map\n",
    "                southArea = L * southX\n",
    "                northArea = oppWpickupFrac * (neededWedgeArea - southArea) + southArea\n",
    "                targetArea = 0.5* (4.*neededWedgeArea - southArea - northArea)  #this is for EAST and WEST wedges only -- see above for north\n",
    "                guessed_XLENGTH = 2.\n",
    "                root = minimize(areaError,[guessed_XLENGTH],args=(L, nHA, targetArea))\n",
    "                eastdX = root.x[0]\n",
    "                eastHalfY = eastdX * tan(nHA)\n",
    "                wedgeR[1] = (eastdX*eastdX + eastHalfY*eastHalfY)**0.5\n",
    "                #print(\"wedgeR[1] =\",round(wedgeR[1],5) )\n",
    "\n",
    "                #northeastPoint = Point(southX, 2.*L)\n",
    "                #southeastPoint = Point(southX, 0.)\n",
    "                #eastTriangle = Polygon([ CP,southeastPoint,northeastPoint ])\n",
    "                #eastNeededArea = eastNeededArea - eastTriangle.area  #this becomes a quadratic in \"eastdX\", the width of east trapezoid\n",
    "                #eastNeededArea = 0.5*eastdX*eastdX*tan(nHA) + (eastdX)*2L\n",
    "                # 0 = 0.5* tan(0.5*(pi-wideAngle)) * (westX-southX)^2 + 2.*L*(westX-southX) - westNeededArea\n",
    "                #a = 0.5 * tan(nHA)\n",
    "                #b = 2.*L                  \n",
    "                #c = -1.*eastNeededArea\n",
    "                #eastdX = ( -1.*b + (b*b - 4.*a*c)**0.5 )/(2.*a)  #quadratic formula, positive root\n",
    "                wedgeR = [L/cos(wHA), eastdX/cos(nHA), L/cos(wHA)*(northArea/southArea)**0.5, eastdX/cos(nHA)]\n",
    "                #print(\"eastdX, wedge Rs are\",round(eastdX,5),wedgeR)\n",
    "\n",
    "            elif np.min(maxArea) - neededWedgeArea < p * neededWedgeArea :   #we are close enough to edge to leave a constrained remnant.  Pick it up.\n",
    "                areaGlut = maxArea[minW] - neededWedgeArea\n",
    "                reducedNeededWedgeArea = neededWedgeArea - areaGlut / 2.  #two adj wedges shrink to accommodate.  For 1-edge, none will hit edge\n",
    "                for w in [int((minW+1)%4), int((minW+3)%4) ] :\n",
    "                    wedgeR[w] = (2.*reducedNeededWedgeArea) ** 0.5  #note: in this case, we are not changing wedge angles.  \"2\" from triangle\n",
    "                wedgeR[minW] = 10.  #this one is unconstrained, to get to boundary.  oppWedge radius is not modified\n",
    "\n",
    "            startAngle = [-0.5*pi-wHA, 0.*pi-nHA, 0.5*pi-wHA, 1.*pi-nHA]\n",
    "            stopAngle =  [-0.5*pi+wHA, 0.*pi+nHA, 0.5*pi+wHA, 1.*pi+nHA]\n",
    "            for w in range(4):\n",
    "                wedgePt2 = Point(CP.x + wedgeR[w] * math.cos(startAngle[w]), CP.y + wedgeR[w] * math.sin(startAngle[w]) )\n",
    "                wedgePt3 = Point(CP.x + wedgeR[w] * math.cos(stopAngle[w]),  CP.y + wedgeR[w] * math.sin(stopAngle[w])  )   \n",
    "                wedgePoly[w] = Polygon([CP, wedgePt2, wedgePt3])\n",
    "\n",
    "            finalPoly = wedgePoly[0].union(wedgePoly[1].union(wedgePoly[2].union(wedgePoly[3]) )  )\n",
    "            if abs(finalPoly.intersection(MAP).area - 4.) > 0.1:\n",
    "                print(\"error!  final Poly area is\", finalPoly.intersection(MAP).area,\"not 4.00\")\n",
    "                pause = input(\"click to stop\")\n",
    "            if yy%50 == -1 :  #0 ; impossible:\n",
    "                print(\"L, areaGlut, wedgeRs are\",L,r5(areaGlut), wedgeR)\n",
    "                print(\"L,finalPoly-MAP area = \",round(L,3),round(finalPoly.intersection(MAP).area,4))  #debug, should equal 2\n",
    "                #plotPoly(finalPoly)\n",
    "                plotPoly(Polygon([Point(-1,0), Point(1,0), Point(1,2), Point(-1,2)]) )           \n",
    "                for w in range(4):\n",
    "                    print(\"wedge no, area \",w, round((wedgePoly[w].intersection(MAP)).area, 5) ) \n",
    "                    plotPoly(wedgePoly[w])\n",
    "                plt.show()\n",
    "                pause = input(\"ready to continue?\")\n",
    "            for yy in range(ySlices):\n",
    "                yUse[yy] += 0.5*yLayer[yy].intersection(finalPoly).area  #0.5 is for normalization (half area was two)\n",
    "        variance = 0.\n",
    "        for yy in range(ySlices): #this loop: sum up the RMSE deviation from target\n",
    "            L = (0.5+yy)*dy\n",
    "            if L < 2.0:  #ignore y's > 2; those won't deviate from target\n",
    "                variance += (yUse[yy] - 1.) **2 * 1.5/ySlices   #1.5 cuz only 2/3 of ySlices will have variance\n",
    "\n",
    "        RMSE3[i] = round(variance **0.5,6)\n",
    "        MAXA = r3(maxAngle[ii]/pi)\n",
    "        print(\"RMS error is\",RMSE3[i],\"for max extra-captured relative wedge area of\",p,\"and maxAngle/pi=\",MAXA )\n",
    "        plt.plot(yCenter,yUse,label=\"max uncap = \"+str(p)+\", maxA/pi=\"+str(MAXA) )\n",
    "plt.xlabel(\"distance from edge\")\n",
    "plt.ylabel(\"relative layer use\")\n",
    "plt.legend(loc=8)\n",
    "plt.title(\"yUse vs. max extra-captured wedge area with levelY, maxWt, oppWpickupFrac = \"+str(levelY)+\",\"+str(maxWt)+\",\"+str(oppWpickupFrac) )\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f38cc9e-1f8c-4744-916b-dd5704d40192",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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